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Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics : Proceedings of the 8th International Workshop on Complex Structures and Vector Fields.

By: Contributor(s): Publisher: Singapore : World Scientific Publishing Co Pte Ltd, 2007Copyright date: ©2007Description: 1 online resource (350 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9789812709806
Subject(s): Genre/Form: Additional physical formats: Print version:: Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics : Proceedings of the 8th International Workshop on Complex Structures and Vector FieldsDDC classification:
  • 515
LOC classification:
  • QA319.I59 2006
Online resources:
Contents:
Intro -- CONTENTS -- Preface -- Organizing Committee -- Contributed Communications -- Moduli space of Killing helices of low orders on a complex space form T. Adachi -- 1. Introduction -- 2. Moduli space of Killing helices and length spectrum -- 3. Moduli space of helices on a real space form -- 4. Moduli space of circles on a complex space form -- 5. Moduli spaces of Killing helices of orders less than 5 on a complex space form -- 6. Lamination on moduli space of essential Killing helices -- Acknowledgments -- References -- Type two Killing helices of proper order four on a complex projective plane T. Adachi and S. Maeda -- 1. Introduction -- 2. Killing helices of proper order 4 -- 3. Type 2 Killing helices -- 4. Limit curves -- References -- Real analyticity of the hyperkahler almost K¨ahler manifolds L.N. Apostolova -- 1. Preliminaries -- 2. Real analyticity of a smooth manifold with two symplectic-homotopic symplectic forms ω0 and ω1 -- 3. Polarization of a symplectic form -- 4. Real analyticity of the hyperkahler almost K¨ahler manifolds -- References -- KCC and linear stability for the Parkinson tremor model V. Balan -- 1. The neural 3-unit feedback model -- 2. The covariant extension. Structural stability -- 3. Linear and KCC stability -- 4. The second-order Lagrangian extension -- Acknowledgement -- References -- The Camassa-Holm equation as a geodesic .ow for the H1 right-invariant metric A. Constantin and R.I. Ivanov -- 1. Motion of a rigid body with a .xed point - the SO(3) example -- 2. Camassa-Holm equation - right invariant metric on the diffeomorphism group -- 3. Inverse Scattering for the CH equation -- 4. Soliton solutions and the diffeomorphisms -- Acknowledgments -- References -- Fermi-Walker parallel transport, time evolution of a space curve and the Schr¨odinger equation as a moving curve R. Dandoloff.
I. Space curves, parallel transport and anholonomy. -- II. Lamb formalism, geometric phase and gauge potential. -- References -- Remarks on bicomplex variables and other similar variables S. Dimiev, R. Lazov and S. Slavova -- 1. Historical notes -- 2. Bicomplex and similar variables - a short recall -- 3. Real matrix representation of C(1, j) and C(1, j, j2, j3) -- 4. Complex quadratic geometries over C(1, j) and C(1, j, j2, j3) -- References -- Integrability, curvature and description of photon-like objects S. Donev and M. Tashkova -- 1. Introduction -- 2. Modelling Photon-like Objects -- 3. Physical Interpretation -- 4. Conclusion -- References -- Complex submanifolds and Lagrangian submanifolds associate with minimal surfaces in tori N. Ejiri -- 1. Introduction -- 2. A review on a function with parameter -- 3. A function with parameter on the Siegel upper half space Hγ -- 4. Minimal surfaces in tori -- References -- About resonances for Schr¨odinger operators with short range singular perturbation V. Georgiev and N. Visciglia -- 1. Introduction -- 2. On the continuity of the operator R(λ ± i0) -- 3. Some preliminary computations -- 4. Proof of theorem 1.1 -- Acknowledgments -- References -- Soliton equations with deep reductions. Generalized Fourier transforms V. Gerdjikov, N. Kostov and T. Valchev -- 1. Introduction -- 2. Preliminaries -- 3. Wronskian relations and squared solutions -- 4. Completeness of the squared solutions -- 5. Expansions over the squared solutions -- 6. Hamiltonian formalism -- 7. Conclusions -- Acknowledgement -- References -- On some deformations of almost complex structures of 6-dimensional submanifolds in the octonions H. Hashimoto -- 1. Introduction -- 2. Clifford algebras, spinor groups and octonions -- 2.1. Clifford algebras and spinor groups -- 2.2. Spin (7)-structure equations -- 3. Gram-Schmidt process of Spin(7).
4. Invariants of Spin(7) -- 5. Homogeneous spaces related to Spin(7) -- 6. Deformations of some examples -- 6.1. On S2 × S4 -- 6.2. On 1-parameter family of embeddings from S2 × R4 to C -- 6.3. On 1-parameter family of embeddings from S1 × S2 × R3 to C -- References -- On the real hypersurfaces of locally conformally-K¨ahler manifolds M.J. Hristov -- 1. Preliminaries -- 1.1. Locally conformally K¨ahler manifolds -- 1.2. Contact conformally almost contact metric manifolds -- 2. Real hypersurfaces of locally conformally-K¨ahler manifolds -- References -- Normal frames and linear transports along paths in line bundles. Applications to classical electrodynamics B.Z. Iliev -- 1. Introduction -- 2. Linear transports along paths (brief review) -- 3. Normal frames for linear transports -- 4. Linear transports and normal frames in line bundles -- 5. Bundle description of the classical electromagnetic field -- 6. Normal and inertial frames -- 7. Conclusion -- References -- Existence and uniqueness results for the Schr¨odinger - Poisson system below the energy norm A.M. Ivanov and G.P. Venkov -- 1. Introduction -- 2. Local existence result in ˙H 1 2 -- 3. Global existence result in H 1 2 -- Acknowledgments -- References -- Double-complex quadratic forms B. Kiradjiev -- 1. Double-complex numbers and double-complex vectors -- 2. Bilinear and quadratic forms on Cn(1, j) -- 3. Double-complex holomorphic Q-orthogonal geometry -- 3.1. Double-complex holomorphicity -- 3.2. Q-orthogonal geometry -- 4. Complex-hermitian double-complex quadratic forms -- 5. Fourth-complex quadratic forms -- References -- Effects of finite arithmetic in numerical computations M.M. Konstantinov and P.H. Petkov -- 1. Introduction -- 2. Myths in computational practice -- 3. Bad and good computational practices -- 3.1. Floating-point computations -- 3.2. Computing determinants.
3.3. Solving linear algebraic equations -- 3.4. Rank determination -- 3.5. Solving algebraic equations -- 3.6. Computing eigenvalues of a matrix -- References -- Exact solutions of the manakov system N.A. Kostov -- 1. Introduction -- 2. Basic equations and solutions -- 3. Exact solutions of the Manakov system using Lax pairs method -- 4. Alternative Theta-functional integration -- 5. Conclusions -- Acknowledgements -- References -- The Manakov system as two moving interacting curves N.A. Kostov, R. Dandolo., V.S. Gerdjikov and G.G. Grahovski -- 1. Introduction -- 2. Preliminaries -- 2.1. The Manakov model -- 2.2. Soliton curves -- 3. Integration of the extended da Rios system -- 4. Extended da Rios-Betchov system -- 5. HF system is gauge equivalent to Manakov system -- 6. Conclusions -- Acknowledgements -- References -- Cluster sets and periodicity in some structure fractals J. Lawrynowicz, S. Marchiafava and M. Nowak-K¸epczyk -- 1. Introduction and statement of the periodicity theorem -- 2. Quaternions and octonions in the Cayley-Dickson construction -- 3. The case 2p 1, period 1. A fractal bundle of the ower type -- 4. The case: 2p 1, perpendicular lower convergence. Ovary and ovules -- 5. The case: 2p 1, perpendicular upper convergence. The pistil and stamens -- References -- Sectional curvatures of some homogeneous real hypersurfaces in a complex projective space S. Maeda and M. Kimura -- 1. Introduction -- 2. Preliminaries -- 3. Sectional curvatures of hypersurfaces of type A or type B -- 4. Pinching problems on sectional curvature of real hypersurfaces -- On three-parametric Lie groups as quasi-K¨ahler manifolds with killing Norden metric M. Manev, K. Gribachev and D. Mekerov -- Introduction -- 1. Almost complex manifolds with Norden metric -- 1.1. Preliminaries -- 1.2. Curvature properties -- 1.3. Isotropic K¨ahler manifolds.
2. Lie groups as quasi-K¨ahler manifolds with Killing Norden metric -- 3. The Lie group as a 6-dimensional W3-manifold -- 4. Geometric characteristics of the constructed manifold -- 4.1. The components of the tensor F -- 4.2. The square norm of ∇J -- 4.3. The components of R -- 4.4. The components of ρ and the value of τ -- 4.5. The sectional curvatures -- 4.6. The isotropic-K¨ahlerian property -- References -- Application of unscented and extended Kalman filtering for estimating quaternion motion V. Markova -- 1. Introduction -- 2. Kalman's filters - short background -- 3. The Problem of Trajectory interpolation -- 4. Experimental Study -- 5. Conclusion -- References -- Counterexamples of compact type to the Goldberg conjecture and various version of the conjecture Y. Matsushita -- 1. The Goldberg conjecture -- 2. Noncompact type for almost Hermitian manifolds -- 3. Noncompact type for almost pseudo-Hermitian manifolds -- 4. Counterexamples of compact type for almost pseudo-Hermitian Walker 8-manifolds -- 5. Almost Norden manifolds -- 6. Almost para-Hermitian manifolds -- 7. Odd-dimensional manifolds -- References -- Dispersion and asymptotic profiles for Kirchhoff equations T. Matsuyama and M. Ruzhansky -- 1. Introduction -- 2. Results -- 3. Representation of solutions to linear Cauchy problems -- References -- Geometry of statistical manifolds and its generalization H. Matsuzoe -- Introduction -- 1. Dual connections -- 2. Statistical manifolds -- 3. A generalization of statistical manifolds -- Acknowledgement -- References -- On some non-integrable almost contact manifolds with norden metric of dimension 5 G. Nakova -- Introduction -- 1. Almost contact manifolds with Norden metric -- 1.1. Preliminaries -- 1.2. Curvature properties -- 2. Lie groups as almost contact manifolds with Norden metric.
3. A Lie group as a 5-dimensional almost contact manifold with Norden metric of the class F9.
Summary: This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas. Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.
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Intro -- CONTENTS -- Preface -- Organizing Committee -- Contributed Communications -- Moduli space of Killing helices of low orders on a complex space form T. Adachi -- 1. Introduction -- 2. Moduli space of Killing helices and length spectrum -- 3. Moduli space of helices on a real space form -- 4. Moduli space of circles on a complex space form -- 5. Moduli spaces of Killing helices of orders less than 5 on a complex space form -- 6. Lamination on moduli space of essential Killing helices -- Acknowledgments -- References -- Type two Killing helices of proper order four on a complex projective plane T. Adachi and S. Maeda -- 1. Introduction -- 2. Killing helices of proper order 4 -- 3. Type 2 Killing helices -- 4. Limit curves -- References -- Real analyticity of the hyperkahler almost K¨ahler manifolds L.N. Apostolova -- 1. Preliminaries -- 2. Real analyticity of a smooth manifold with two symplectic-homotopic symplectic forms ω0 and ω1 -- 3. Polarization of a symplectic form -- 4. Real analyticity of the hyperkahler almost K¨ahler manifolds -- References -- KCC and linear stability for the Parkinson tremor model V. Balan -- 1. The neural 3-unit feedback model -- 2. The covariant extension. Structural stability -- 3. Linear and KCC stability -- 4. The second-order Lagrangian extension -- Acknowledgement -- References -- The Camassa-Holm equation as a geodesic .ow for the H1 right-invariant metric A. Constantin and R.I. Ivanov -- 1. Motion of a rigid body with a .xed point - the SO(3) example -- 2. Camassa-Holm equation - right invariant metric on the diffeomorphism group -- 3. Inverse Scattering for the CH equation -- 4. Soliton solutions and the diffeomorphisms -- Acknowledgments -- References -- Fermi-Walker parallel transport, time evolution of a space curve and the Schr¨odinger equation as a moving curve R. Dandoloff.

I. Space curves, parallel transport and anholonomy. -- II. Lamb formalism, geometric phase and gauge potential. -- References -- Remarks on bicomplex variables and other similar variables S. Dimiev, R. Lazov and S. Slavova -- 1. Historical notes -- 2. Bicomplex and similar variables - a short recall -- 3. Real matrix representation of C(1, j) and C(1, j, j2, j3) -- 4. Complex quadratic geometries over C(1, j) and C(1, j, j2, j3) -- References -- Integrability, curvature and description of photon-like objects S. Donev and M. Tashkova -- 1. Introduction -- 2. Modelling Photon-like Objects -- 3. Physical Interpretation -- 4. Conclusion -- References -- Complex submanifolds and Lagrangian submanifolds associate with minimal surfaces in tori N. Ejiri -- 1. Introduction -- 2. A review on a function with parameter -- 3. A function with parameter on the Siegel upper half space Hγ -- 4. Minimal surfaces in tori -- References -- About resonances for Schr¨odinger operators with short range singular perturbation V. Georgiev and N. Visciglia -- 1. Introduction -- 2. On the continuity of the operator R(λ ± i0) -- 3. Some preliminary computations -- 4. Proof of theorem 1.1 -- Acknowledgments -- References -- Soliton equations with deep reductions. Generalized Fourier transforms V. Gerdjikov, N. Kostov and T. Valchev -- 1. Introduction -- 2. Preliminaries -- 3. Wronskian relations and squared solutions -- 4. Completeness of the squared solutions -- 5. Expansions over the squared solutions -- 6. Hamiltonian formalism -- 7. Conclusions -- Acknowledgement -- References -- On some deformations of almost complex structures of 6-dimensional submanifolds in the octonions H. Hashimoto -- 1. Introduction -- 2. Clifford algebras, spinor groups and octonions -- 2.1. Clifford algebras and spinor groups -- 2.2. Spin (7)-structure equations -- 3. Gram-Schmidt process of Spin(7).

4. Invariants of Spin(7) -- 5. Homogeneous spaces related to Spin(7) -- 6. Deformations of some examples -- 6.1. On S2 × S4 -- 6.2. On 1-parameter family of embeddings from S2 × R4 to C -- 6.3. On 1-parameter family of embeddings from S1 × S2 × R3 to C -- References -- On the real hypersurfaces of locally conformally-K¨ahler manifolds M.J. Hristov -- 1. Preliminaries -- 1.1. Locally conformally K¨ahler manifolds -- 1.2. Contact conformally almost contact metric manifolds -- 2. Real hypersurfaces of locally conformally-K¨ahler manifolds -- References -- Normal frames and linear transports along paths in line bundles. Applications to classical electrodynamics B.Z. Iliev -- 1. Introduction -- 2. Linear transports along paths (brief review) -- 3. Normal frames for linear transports -- 4. Linear transports and normal frames in line bundles -- 5. Bundle description of the classical electromagnetic field -- 6. Normal and inertial frames -- 7. Conclusion -- References -- Existence and uniqueness results for the Schr¨odinger - Poisson system below the energy norm A.M. Ivanov and G.P. Venkov -- 1. Introduction -- 2. Local existence result in ˙H 1 2 -- 3. Global existence result in H 1 2 -- Acknowledgments -- References -- Double-complex quadratic forms B. Kiradjiev -- 1. Double-complex numbers and double-complex vectors -- 2. Bilinear and quadratic forms on Cn(1, j) -- 3. Double-complex holomorphic Q-orthogonal geometry -- 3.1. Double-complex holomorphicity -- 3.2. Q-orthogonal geometry -- 4. Complex-hermitian double-complex quadratic forms -- 5. Fourth-complex quadratic forms -- References -- Effects of finite arithmetic in numerical computations M.M. Konstantinov and P.H. Petkov -- 1. Introduction -- 2. Myths in computational practice -- 3. Bad and good computational practices -- 3.1. Floating-point computations -- 3.2. Computing determinants.

3.3. Solving linear algebraic equations -- 3.4. Rank determination -- 3.5. Solving algebraic equations -- 3.6. Computing eigenvalues of a matrix -- References -- Exact solutions of the manakov system N.A. Kostov -- 1. Introduction -- 2. Basic equations and solutions -- 3. Exact solutions of the Manakov system using Lax pairs method -- 4. Alternative Theta-functional integration -- 5. Conclusions -- Acknowledgements -- References -- The Manakov system as two moving interacting curves N.A. Kostov, R. Dandolo., V.S. Gerdjikov and G.G. Grahovski -- 1. Introduction -- 2. Preliminaries -- 2.1. The Manakov model -- 2.2. Soliton curves -- 3. Integration of the extended da Rios system -- 4. Extended da Rios-Betchov system -- 5. HF system is gauge equivalent to Manakov system -- 6. Conclusions -- Acknowledgements -- References -- Cluster sets and periodicity in some structure fractals J. Lawrynowicz, S. Marchiafava and M. Nowak-K¸epczyk -- 1. Introduction and statement of the periodicity theorem -- 2. Quaternions and octonions in the Cayley-Dickson construction -- 3. The case 2p 1, period 1. A fractal bundle of the ower type -- 4. The case: 2p 1, perpendicular lower convergence. Ovary and ovules -- 5. The case: 2p 1, perpendicular upper convergence. The pistil and stamens -- References -- Sectional curvatures of some homogeneous real hypersurfaces in a complex projective space S. Maeda and M. Kimura -- 1. Introduction -- 2. Preliminaries -- 3. Sectional curvatures of hypersurfaces of type A or type B -- 4. Pinching problems on sectional curvature of real hypersurfaces -- On three-parametric Lie groups as quasi-K¨ahler manifolds with killing Norden metric M. Manev, K. Gribachev and D. Mekerov -- Introduction -- 1. Almost complex manifolds with Norden metric -- 1.1. Preliminaries -- 1.2. Curvature properties -- 1.3. Isotropic K¨ahler manifolds.

2. Lie groups as quasi-K¨ahler manifolds with Killing Norden metric -- 3. The Lie group as a 6-dimensional W3-manifold -- 4. Geometric characteristics of the constructed manifold -- 4.1. The components of the tensor F -- 4.2. The square norm of ∇J -- 4.3. The components of R -- 4.4. The components of ρ and the value of τ -- 4.5. The sectional curvatures -- 4.6. The isotropic-K¨ahlerian property -- References -- Application of unscented and extended Kalman filtering for estimating quaternion motion V. Markova -- 1. Introduction -- 2. Kalman's filters - short background -- 3. The Problem of Trajectory interpolation -- 4. Experimental Study -- 5. Conclusion -- References -- Counterexamples of compact type to the Goldberg conjecture and various version of the conjecture Y. Matsushita -- 1. The Goldberg conjecture -- 2. Noncompact type for almost Hermitian manifolds -- 3. Noncompact type for almost pseudo-Hermitian manifolds -- 4. Counterexamples of compact type for almost pseudo-Hermitian Walker 8-manifolds -- 5. Almost Norden manifolds -- 6. Almost para-Hermitian manifolds -- 7. Odd-dimensional manifolds -- References -- Dispersion and asymptotic profiles for Kirchhoff equations T. Matsuyama and M. Ruzhansky -- 1. Introduction -- 2. Results -- 3. Representation of solutions to linear Cauchy problems -- References -- Geometry of statistical manifolds and its generalization H. Matsuzoe -- Introduction -- 1. Dual connections -- 2. Statistical manifolds -- 3. A generalization of statistical manifolds -- Acknowledgement -- References -- On some non-integrable almost contact manifolds with norden metric of dimension 5 G. Nakova -- Introduction -- 1. Almost contact manifolds with Norden metric -- 1.1. Preliminaries -- 1.2. Curvature properties -- 2. Lie groups as almost contact manifolds with Norden metric.

3. A Lie group as a 5-dimensional almost contact manifold with Norden metric of the class F9.

This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas. Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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