Perspectives of complex analysis, differential geometry and mathematical physics

✍ Scribed by Dimiev S., Sekigawa K. (eds.)

• Publisher: WS
• Year: 2001
• Tongue: English
• Leaves: 220
• Category: Library

✦ Synopsis

This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings should be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields.

✦ Table of Contents

Preface......Page 8
CONTENTS......Page 10
1 Introduction......Page 12
2 Definitions and known facts......Page 14
3 The basic result......Page 17
4 Proof of Theorem 14......Page 22
5 Case A)......Page 32
6 Case C)......Page 39
7 Case B)......Page 41
8 Case D)......Page 44
References......Page 45
1 Introduction......Page 47
2 Hahn-Banach type theorems......Page 49
3 Proofs......Page 52
4 Extension of invariant differential forms......Page 53
References......Page 55
The Theorem on Analytic Representation on Hypersurface with Singularities......Page 56
References......Page 63
1 Recall of definitions......Page 64
2 Pseudogroup structures......Page 65
3 T-manifolds integrability of (M J)......Page 67
References......Page 68
1 Introduction......Page 69
2 Dualities......Page 71
3 Complementarity......Page 73
References......Page 83
1 Introduction......Page 86
2 Preliminaries......Page 87
3 Embedding and IGL1(C)-actions......Page 88
References......Page 90
1 Introduction......Page 91
2 Notation......Page 92
3 The quotient spaces in Massey's diagram......Page 93
4 Other quotient spaces in the complete diagram......Page 94
5 Problems......Page 95
References......Page 96
1 Introduction......Page 97
2 Preliminaries......Page 98
3 Proof of Theorem 1.1......Page 100
References......Page 103
2 Geodesic spheres and tubes around hyperplanes......Page 104
3 Length spectrum from qualitative viewpoint......Page 106
4 Length spectrum from quantitative viewpoint......Page 107
5 Structure torsion of geodesics......Page 109
6 Congruency of geodesics......Page 111
7 Sketch of Proofs......Page 114
References......Page 122
1 Preliminaries......Page 124
2 J-holomorphic curves......Page 127
3 3-dimensional submanifolds......Page 130
4 4-dimensional submanifolds......Page 133
References......Page 134
1 Introduction......Page 136
2 Spheres of codimension two in Euclidean space......Page 137
3 One-parameter families of spheres of codimension two in En + 1......Page 139
References......Page 145
1 Preliminaries......Page 146
2 Hypersurfaces of conullity two in Euclidean space......Page 147
3 Torses in Euclidean space......Page 150
4 Hypersurfaces of conullity two and one-parameter systems of torses......Page 153
References......Page 157
1 Introduction......Page 158
2 The sixteen possible classes of real hypersurfaces of a Kaehler manifold......Page 162
3 Examples......Page 166
References......Page 168
1 Preliminaries......Page 170
2 Time-like hypersurfaces of an almost complex manifold with B-metric......Page 173
3 Isotropic hypersurfaces regarding the associated metric of an almost complex manifold with B-metric......Page 178
References......Page 181
1 Introduction and statement of the investigated problem......Page 182
2 First and Second Differentials and Variations......Page 184
3 Formulation of the Variational Problem in the Case of Different Operators of Variation and Differentiation......Page 185
4 First Variation of the Lagrangian as a Third-Rank Polynomial......Page 186
5 Third-Rank Polynomials - Formulation of the Problem from an Algebro-Geometric Point of View......Page 188
References......Page 189
2 Geometrical framework......Page 191
3 Symmetry......Page 192
4 Main Conjecture......Page 193
5 Field Equations......Page 195
6 General Physical Interpretation......Page 198
7 Summary......Page 199
References......Page 200
1 Introduction......Page 201
2 Lagrangian density and Lagrangian invariant......Page 203
3 Euler-Lagrange's equations for the variables on which the pressure p depends......Page 205
4 Energy-momentum tensors for a fluid with pressure p......Page 208
References......Page 210
1 Preliminary......Page 212
2 (v)-Corresponding Affine Connectedness......Page 215
3 Mutual Connectedness......Page 217
References......Page 219