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

CONTENTS......Page 12
Preface......Page 6
Organizing Committee......Page 8
Contributed Communications......Page 9
1. Introduction......Page 16
3. Moduli space of helices on a real space form......Page 17
4. Moduli space of circles on a complex space form......Page 18
5. Moduli spaces of Killing helices of orders less than 5 on a complex space form......Page 20
6. Lamination on moduli space of essential Killing helices......Page 21
References......Page 23
1. Introduction......Page 24
3. Type 2 Killing helices......Page 25
4. Limit curves......Page 28
References......Page 29
1. Preliminaries......Page 30
2. Real analyticity of a smooth manifold with two symplectic-homotopic symplectic forms ω0 and ω1......Page 31
3. Polarization of a symplectic form......Page 35
4. Real analyticity of the hyperkahler almost Kähler manifolds......Page 36
References......Page 37
1. The neural 3-unit feedback model......Page 38
2. The covariant extension. Structural stability......Page 39
3. Linear and KCC stability......Page 43
4. The second-order Lagrangian extension......Page 45
Acknowledgement......Page 46
References......Page 47
1. Motion of a rigid body with a fixed point — the SO(3) example......Page 48
2. Camassa-Holm equation – right invariant metric on the diffeomorphism group......Page 50
3. Inverse Scattering for the CH equation......Page 52
4. Soliton solutions and the diffeomorphisms......Page 54
References......Page 55
I. Space curves, parallel transport and anholonomy.......Page 57
II. Lamb formalism, geometric phase and gauge potential.......Page 59
References......Page 64
1. Historical notes......Page 65
2. Bicomplex and similar variables — a short recall......Page 67
4. Complex quadratic geometries over C(1, j) and C(1, j, j2, j3)......Page 69
References......Page 70
1. Introduction......Page 72
2. Modelling Photon-like Objects......Page 74
3. Physical Interpretation......Page 78
References......Page 80
1. Introduction......Page 81
2. A review on a function with parameter......Page 82
3. A function with parameter on the Siegel upper half space Hγ......Page 83
4. Minimal surfaces in tori......Page 85
References......Page 88
1. Introduction......Page 89
2. On the continuity of the operator R(λ ± i0)......Page 93
3. Some preliminary computations......Page 94
4. Proof of theorem 1.1......Page 97
References......Page 99
1. Introduction......Page 100
2. Preliminaries......Page 101
3. Wronskian relations and squared solutions......Page 105
4. Completeness of the squared solutions......Page 106
5. Expansions over the squared solutions......Page 108
6. Hamiltonian formalism......Page 109
References......Page 110
1. Introduction......Page 112
2.1. Clifford algebras and spinor groups......Page 113
2.2. Spin (7)-structure equations......Page 115
3. Gram-Schmidt process of Spin(7)......Page 116
4. Invariants of Spin(7)......Page 117
6.1. On S2 × S4......Page 119
6.2. On 1-parameter family of embeddings from S2 × R4 to C......Page 121
6.3. On 1-parameter family of embeddings from S1 × S2 × R3 to C......Page 123
References......Page 124
1.1. Locally conformally Kähler manifolds......Page 125
1.2. Contact conformally almost contact metric manifolds......Page 128
2. Real hypersurfaces of locally conformally-Kähler manifolds......Page 130
References......Page 132
1. Introduction......Page 134
2. Linear transports along paths (brief review)......Page 135
3. Normal frames for linear transports......Page 136
4. Linear transports and normal frames in line bundles......Page 138
5. Bundle description of the classical electromagnetic field......Page 139
6. Normal and inertial frames......Page 141
References......Page 143
1. Introduction......Page 145
2. Local existence result in H 1/2......Page 147
3. Global existence result in H 1/2......Page 150
References......Page 152
1. Double-complex numbers and double-complex vectors......Page 153
2. Bilinear and quadratic forms on Cn(1, j)......Page 155
3.1. Double-complex holomorphicity......Page 156
3.2. Q-orthogonal geometry......Page 158
5. Fourth-complex quadratic forms......Page 159
References......Page 160
1. Introduction......Page 161
2. Myths in computational practice......Page 162
3.1. Floating-point computations......Page 166
3.2. Computing determinants......Page 167
3.3. Solving linear algebraic equations......Page 168
3.4. Rank determination......Page 169
3.5. Solving algebraic equations......Page 170
3.6. Computing eigenvalues of a matrix......Page 171
References......Page 172
2. Basic equations and solutions......Page 173
3. Exact solutions of the Manakov system using Lax pairs method......Page 177
4. Alternative Theta-functional integration......Page 180
References......Page 181
1. Introduction......Page 183
2.1. The Manakov model......Page 184
2.2. Soliton curves......Page 185
3. Integration of the extended da Rios system......Page 186
4. Extended da Rios-Betchov system......Page 190
6. Conclusions......Page 191
References......Page 192
Cluster sets and periodicity in some structure fractals J. Lawrynowicz, S. Marchiafava and M. Nowak-Kepczyk......Page 194
1. Introduction and statement of the periodicity theorem......Page 195
2. Quaternions and octonions in the Cayley-Dickson construction......Page 199
4. The case: α≤2p – 1, perpendicular lower convergence. Ovary and ovules......Page 201
5. The case: α≤2p – 1, perpendicular upper convergence. The pistil and stamens......Page 207
References......Page 209
1. Introduction......Page 211
2. Preliminaries......Page 212
3. Sectional curvatures of hypersurfaces of type A or type B......Page 214
4. Pinching problems on sectional curvature of real hypersurfaces......Page 218
Introduction......Page 220
1.1. Preliminaries......Page 221
1.3. Isotropic Kähler manifolds......Page 222
2. Lie groups as quasi-Kähler manifolds with Killing Norden metric......Page 223
3. The Lie group as a 6-dimensional W3-manifold......Page 224
4.1. The components of the tensor F......Page 226
4.3. The components of R......Page 227
4.6. The isotropic-Kählerian property......Page 228
References......Page 229
1. Introduction......Page 230
2. Kalman’s filters - short background......Page 232
3. The Problem of Trajectory interpolation......Page 233
4. Experimental Study......Page 234
References......Page 236
1. The Goldberg conjecture......Page 237
3. Noncompact type for almost pseudo-Hermitian manifolds......Page 238
4. Counterexamples of compact type for almost pseudo-Hermitian Walker 8-manifolds......Page 240
6. Almost para-Hermitian manifolds......Page 245
References......Page 247
1. Introduction......Page 249
2. Results......Page 252
3. Representation of solutions to linear Cauchy problems......Page 254
References......Page 257
Introduction......Page 259
1. Dual connections......Page 260
2. Statistical manifolds......Page 262
3. A generalization of statistical manifolds......Page 264
References......Page 266
1.1. Preliminaries......Page 267
1.2. Curvature properties......Page 268
2. Lie groups as almost contact manifolds with Norden metric......Page 269
3. A Lie group as a 5-dimensional almost contact manifold with Norden metric of the class F9......Page 272
4. Curvature properties of the constructed manifold......Page 274
References......Page 275
0. Introduction......Page 276
1. Preliminaries, notations (cf. [2,3])......Page 277
2. Complexification......Page 278
References......Page 283
1. Introduction......Page 284
2. Preliminaries......Page 286
3. Critical point of Fλ,μ......Page 287
References......Page 292
1. Introduction......Page 293
2. Proof of the main results......Page 301
References......Page 304
1. Riemannian almost product manifolds......Page 305
2. A Lie group as a four-dimensional Riemannian P-manifold......Page 307
3. A Lie group as a four-dimensional Riemannian product W2-manifold......Page 310
References......Page 312
1. Elements of the calculus of double-complex di.erential 1-forms of many double-complex variables......Page 314
2. The equation ∂∂*f = 0......Page 316
3. Quadratic geometry on Cn(1, j)......Page 319
4. Complex-hermitian double-complex quadratic forms......Page 320
References......Page 322
2. Totally umbilic immersions and order 2 property......Page 323
3. Kähler isometric immersions and order 2 property......Page 326
4. Immersions of rank one symmetric spaces into real space forms......Page 327
5. Isotropic immersions and curvature logarithmic derivatives......Page 330
References......Page 332
1. Almost complex manifolds with Norden metric......Page 334
2. A Lie group as a four-dimensional conformal Kähler manifold with Norden metric......Page 337
References......Page 341
1.1. Bäcklund transformations and inverse scattering method......Page 342
1.2. Riemann-Hilbert problem......Page 345
2. Singular solutions of RHP with additional symmetries......Page 346
References......Page 349
Author Index......Page 350