Trends in Differential Geometry, Complex Analysis and Mathematical Physics: Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields

by Sekigawa, Kouei; Gerdjikov, Vladimir S.; Dimiev, Stancho

• ISBN13: 9789814277716
• ISBN10: 9814277711
• Format: Hardcover
• Copyright: 2009-08-21
• Publisher: World Scientific Pub Co Inc

Summary

This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by CamassaHolm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.

Table of Contents

Preface	p. v
Organizing Committees	p. vii
Presentations	p. ix
A discrete model for Kähler magnetic fields on a complex hyperbolic space	p. 1
Integrability condition on the boundary parameters of the asymmetric exclusion process and matrix product ansatz	p. 10
Remarks on the double-complex Laplacian	p. 20
Generalizations of conjugate connections	p. 26
Asymptotics of generalized value distribution for Herglotz functions	p. 35
Cyclic hyper-scalar systems	p. 46
Plane curves associated with integrable dynamical systems of the Frenet-Serret type	p. 57
Relativistic strain and electromagnetic photon-like objects	p. 64
A construction of minimal surfaces in flat tori by swelling	p. 74
On NLS equations on BD.I symmetric spaces with constant boundary conditions	p. 83
Orthogonal almost complex structures on S2 × R4	p. 92
Persistence of solutions for some integrable shallow water equations	p. 99
Some geometric properties and objects related to Bézier curves	p. 109
Heisenberg relations in the general case	p. 120
Poisson structures of equations associated with groups of diffeomorphisms	p. 131
Hyperbolic Gauss maps and parallel surfaces in hyperbolic three-space	p. 139
On the lax pair for two and three wave interaction system	p. 149
Mathematical outlook of fractals and chaos related to simple orthorhombic Ising-Onsager-Zhang lattices	p. 156
A characterization of Clifford minimal hyper surfaces of a sphere in terms of their geodesies	p. 167
On the curvature properties of real time-like hypersurfaces of Kähler manifolds with Norden metric	p. 174
Some submanifolds of almost contact manifolds with Norden metric	p. 185
A short note on the double-complex Laplace operator	p. 195
Monogenic, hypermonogenic and holomorphic Cliffordian functions - A survey	p. 199
On some classes of exact solutions of eikonal equation	p. 210
Dirichlet property for tessellations of tiling-type 4 on a plane by congrent pentagons	p. 219
Almost complex connections on almost complex manifolds with Norden metric	p. 231
Pseudo-boson coherent and Fock states	p. 241
New integrable equations of mKdV type	p. 251
Integrable dynamical systems of the Frenet-Serret type	p. 261
Author Index	p. 273
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