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

✍ Scribed by Kouei Sekigawa, Vladimir S. Gerdjikov, Stancho Dimiev

• Publisher: World Scientific Pub Co Inc
• Year: 2009
• Tongue: English
• Leaves: 291
• Category: Library

✦ Synopsis

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 Camassa-Holm 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

CONTENTS......Page 14
Preface......Page 6
Organizing Committees......Page 8
Presentations......Page 10
1. Introduction......Page 18
2. Kahler magnetic fields on complex hyperbolic spaces......Page 19
3. Graphs of K ahler type......Page 20
4. Counting prime cycles......Page 23
References......Page 26
1. Introduction......Page 27
2. Matrix Product State Ansatz (MPA)......Page 29
3. Detailed Balance and MPA......Page 33
References......Page 35
1. Double-complex Laplace operator......Page 37
3. D'Alamber's type formula for the initial value problem in the whole space C(1; j)......Page 39
4. Real representation of the equation +u = 0......Page 40
References......Page 42
Introduction......Page 43
1. Generalizations of conjugate connections......Page 44
3. Local triviality of generalized conjugate connections and equia ne structures......Page 47
References......Page 51
1. Introduction......Page 52
2. Herglotz functions and their integral representation......Page 53
3. Value distribution for Herglotz functions......Page 56
References......Page 62
Cyclic hyper-scalar systems S. Dimiev, M.S. Marinov, Z. Zhelev......Page 63
1. Hyper-real systems: K = R......Page 64
3. Real double-variables or para-complex variables......Page 65
4. Four real variables, K = R......Page 66
5. Four-real functions of four real variables......Page 67
6. Partial derivatives with respect to the double-real variables and......Page 68
7. Para-complex di erentiability......Page 69
8. Hyper four-dimensional real scalar Hankel geometry [2–4]......Page 71
Acknowledgments......Page 72
References......Page 73
1. Dynamical systems of the Frenet-Serret type......Page 74
2. Levy's elasticae......Page 75
3. Profile curves of Delaunay's surfaces......Page 78
References......Page 80
1. Strain......Page 81
2. The Concept of photon-like object(s)......Page 82
3. The Electromagnetic strain tensors......Page 84
4. Discussion......Page 87
5. Conclusion......Page 89
References......Page 90
1. Introduction......Page 91
2. Preliminary......Page 92
3. Minimal surfaces in Riemannian at tori......Page 94
References......Page 98
2. MNLS eqs on BD.I-symmetric spaces......Page 100
4. Spectral properties of BD.I-type MNLS with CBC......Page 102
References......Page 107
2. Preliminaries......Page 109
3. Hypersurfaces in ImC......Page 110
4. On G frame eld on S2 R4......Page 111
5. Orbits related to G......Page 113
References......Page 115
1. Introduction......Page 116
2. The b-equations......Page 117
2.1. Compactly supported solutions......Page 119
2.2. Soliton-type solutions......Page 120
References......Page 124
1.1. Barycentric coordinates and barycentric trajectories......Page 126
1.2. Barycentric characterization of the duality in the projective plane. Projective isotomic conjugation......Page 128
2. Bezier curves and related geometric properties and objects......Page 130
References......Page 136
1. Introduction......Page 137
2. The Poincar e group......Page 138
3. Internal transformations......Page 140
4. The general case......Page 141
5. Fibre bundle approach......Page 143
References......Page 146
1. Camassa-Holm equation......Page 148
2. n-dimensional EP Diff equations......Page 151
3. Reduction to the subgroup of volume-preserving diffeomorphisms......Page 153
References......Page 154
1. Introduction......Page 156
2. Basic items......Page 157
3. Parallel surface......Page 159
4. Linear Weingarten surface......Page 162
References......Page 164
1. Two-wave interaction system and monomer......Page 166
2. Three-wave interaction system......Page 170
Acknowledgements......Page 171
References......Page 172
Mathematical outlook of fractals and chaos related to simple orthorhombic Ising-Onsager-Zhang lattices J. Lawrynowicz, S. Marchiafava, M. Nowak-K epczyk......Page 173
1. Introduction and relationship with Bethe-type fractals......Page 174
3. Ising-Onsager-Zhang lattices vs. Jordan-von Neumann-Wigner approach......Page 176
4. The use of fractals of the algebraic structure......Page 180
5. Further perspectives......Page 181
References......Page 182
1. Introduction......Page 184
2. Geodesics on Cli ord hypersurfaces......Page 185
3. Statements of resuls......Page 186
References......Page 190
Introduction......Page 191
1.1. Almost complex manifolds with Norden metric......Page 192
1.2. Almost contact manifolds with Norden metric......Page 193
2. Curvatures on the real time-like hypersurfaces of a K ahler manifold with Norden metric......Page 195
3. Curvatures on W0's real time-like hypersurfaces, belonging to the main classes......Page 198
References......Page 201
1. Introduction......Page 202
2. Submanifolds of codimension 2 of almost contact manifolds with Norden metric with totally real non-orthogonal to normal spaces......Page 203
3. Submanifolds of codimension 2 of almost contact manifolds with Norden metric with totally real orthogonal to normal spaces......Page 205
4. Examples of submanifolds of codimension 2 of almost contact manifolds with Norden metric with totally real normal spaces......Page 206
References......Page 211
1. Introduction and formulation of the main results......Page 212
References......Page 215
1. Clifford algebras......Page 216
2. Generalizations of the one complex variable theory......Page 218
References......Page 226
1. Introduction......Page 227
2. The main idea of decomposition method......Page 228
3. An extension of decomposition method......Page 230
4. Some applications to quantum mechanics......Page 232
6. Resources......Page 234
References......Page 235
1. Introduction......Page 236
2. Dirichlet tessellations......Page 237
3. A tessellation of tiling-type 4 by congruent pentagons......Page 238
4. Dirichlet property......Page 240
5. A tessellation of semi-tiling type 4......Page 242
6. Other tessellations by congruent pentagons......Page 243
References......Page 247
Introduction......Page 249
1. Preliminaries......Page 250
2. Almost complex connections on almost complex manifolds with Norden metric......Page 252
3. Complex connections on conformal K ahler manifolds with Norden metric......Page 255
References......Page 258
1. Introduction......Page 259
2. Pseudo-boson ladder operators......Page 260
3. Pseudo-boson Fock states......Page 262
4. Pseudo-boson coherent states......Page 263
5.1. Pseudo-boson Fock state wave functions......Page 264
5.2. Pseudo-boson CS wave functions......Page 266
References......Page 268
1. Introduction......Page 269
2. Some facts from the theory of solitons......Page 270
3. Multicomponent mKdV associated with symmetric spaces of BD:I series......Page 273
References......Page 278
1. Introduction......Page 279
2. Variational Symmetries......Page 282
3. Conservation Laws......Page 283
4. Group Classification......Page 284
5. Integrable Systems......Page 287
6. Concluding Remarks......Page 288
References......Page 289
Author Index......Page 291