Contemporary aspects of complex analysis, differential geometry, and mathematical physics: proceedings of the 7th International Workshop on Complex Structures and Vector Fields, Plovdiv, Bulgaria, 31 August – 4 September 2004

Stancho Dimiev, Kouei Sekigawa9789812563903, 981-256-390-3

This volume presents the cutting-edge contributions to the Seventh International Workshop on Complex Structures and Vector Fields, which was organized as a continuation of the high successful preceding workshops on similar research. The volume includes works treating ambitious topics in differential geometry, mathematical physics and technology such as Bezier curves in space forms, potential and catastrophy of a soap film, computer-assisted studies of logistic maps, and robotics.

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Table of contents :
CONTENTS……Page 8
Preface……Page 6
Contributed Communications……Page 12
1. Introduction……Page 16
2. Variations of trajectories……Page 17
3. Variations of magnetic fields……Page 21
4. Ruled real surfaces associated with trajectories……Page 22
5. A comparison on crescents……Page 25
References……Page 28
1. Introduction……Page 29
2. Killing ordinary helices on nonflat complex space forms……Page 30
3. Bounded Killing ordinary helices on a complex hyperbolic plane……Page 33
4. Killing ordinary helices on other symmetric spaces of rank one……Page 34
5. Characterization of real space forms by Killing ordinary helices……Page 36
6. A construction of a closed non-Killing ordinary helix on CP”(c)……Page 37
References……Page 38
1. Introduction and some definitions……Page 40
2. Canonical construction……Page 42
3. Real analyticity of the almost Kahler manifolds……Page 44
References……Page 45
1. Introduction……Page 46
2. Terminology……Page 47
3. Isotropic immersions of a sphere into a real space form……Page 48
4. Isotropic immersions of a complex space form into a real space form……Page 51
5. Isotropic immersions of Cayley projective plane into a real space form……Page 53
References……Page 54
1. Introduction……Page 56
2. Even dimensional real anti-cyclic numbers……Page 57
4. Holomorphic functions on C [1,j]……Page 58
6. Cauchy’s integral formula……Page 59
7. Bi-complex analytic functions……Page 61
8. Singularities……Page 62
References……Page 63
1. Definition of the General Parallelism Concept……Page 64
2.1.2. Absolute and relative integral invariants……Page 66
2.1.3. Symplectic mechanics……Page 67
2.2.2. Linear connections……Page 68
2.2.3. Covariant exterior derivative……Page 69
3.1. Autoparallel vector fields and 1-forms……Page 70
3.2.1. Maxwell equations……Page 72
3.2.2. Extended Maxwell equations……Page 73
3.3.1. Extended Yang-Mills equations……Page 74
3.4. General Relativity……Page 75
3.6. Dirac equation……Page 76
4. Conclusion……Page 77
References……Page 78
1. Introduction……Page 79
2. Complex subspaces in RN……Page 80
3. The definition of s-isotropic minimal surfaces……Page 81
4. A deformation by SO(N, C)……Page 85
References……Page 87
1. Introduction……Page 89
2. The Procedure……Page 90
3.1. Non linearities of the form f(ux)……Page 93
3.3. Nonlinearity of the form f(u), f(u)……Page 94
References……Page 95
1. Preliminaries……Page 96
2. Orthogonal compositions in a four-dimensional Weyl space……Page 100
3. Properties of the curvature tensor on a four-dimensional Weyl product space……Page 108
References……Page 113
1. Introduction……Page 115
2. Hamilton description of classical mechanics (review)……Page 116
3. Bundle description of dynamical functions in classical mechanics……Page 117
4. Bundle description of the Liouville equation……Page 120
5. Conclusion……Page 121
References……Page 122
1. Introduction……Page 124
2. Preliminaries……Page 125
3. Obstructions……Page 126
4.1. Ricci-flat case……Page 128
4.3. Scalar-flat case……Page 129
4.4. Constant scalar curvature case……Page 130
5. Problems and questions……Page 131
References……Page 132
1. Introduction……Page 135
2. BQzier curves……Page 136
3. Rational BQzier curves……Page 137
4. Projective Bezier curves on a standard sphere……Page 139
5. Projective Bezier curves on a real hyperbolic plane……Page 143
References……Page 146
1. Background material for stability of vector bundles……Page 147
2. Gieseker stability and canonical metrics……Page 148
3. Harder-Narasimhan filtration……Page 156
4. The case of surfaces……Page 160
References……Page 163
1. Introduction In differential geometry it is interesting to……Page 164
2. Characterization of totally umbilic hypersurfaces I……Page 165
3. Characterizations of isoparametric hypersurfaces……Page 167
4. Characterization of totally umbilic hypersurfaces II……Page 170
References……Page 172
Type-changing transformations of Hurwitz pairs, quasiregular functions, and hyper-Kahlerian holomorphic chains J. Lawrynowicz, M. Nowak and L. Tovar……Page 173
1. Introduction……Page 174
2. Branch-type fractal representation and Atomization Theorem for Hermitian Hurwitz pairs……Page 175
3. Fractal gemmae, their type-changing transformations and the corresponding Atomization Theorem……Page 179
4. Relationship with hyperkahlerian holomorphic chains……Page 184
References……Page 187
Introduction……Page 189
2. Engel manifolds with almost ( H, G)-structure……Page 192
2.1. Double isotropic hyper-Kahlerian structures but neither hypercomplex nor symplectic……Page 193
2.2. Double isotropic hyper-Kahlerian structures which are non-integrable but symplectic……Page 194
3.2. Real quarter-space with almost ( H, G ) -structure……Page 195
4. Real pseudo-hyper-cylinder with almost ( H, G)-structure……Page 196
5.1. Complex cylinder with almost ( H, G)-structure……Page 197
5.3. Complex sphere with almost ( H, G)-structure……Page 198
6.2. A Lie group as a flat Kahler manifold but non-hypercomplex one……Page 200
References……Page 201
1. Introduction……Page 202
2. Navier-Stokes’ identities and Navier-Stokes’ equations……Page 204
3.1. Navier-Stokes’ equations and Euler-Lagmnge’s equations……Page 207
3.2. Representation of F and……Page 208
3.3. Radial projections of Navier-Stokes’ equation. Navier-Stokes’ equation for radial accelerations……Page 209
3.4. Tangential projections of Navier-Stokes’ equation. Navier-Stokes’ equation for tangential accelerations……Page 210
References……Page 211
1. Introduction……Page 212
2. Quaternionic solution of the inverse kinematics problem for planar robot……Page 213
2.1. Quaternionic solution of the inverse kinematics problem for a two link planar robot……Page 214
3.1. Frenet frames in H……Page 216
3.2. Standart protein geometry……Page 218
4. The molecule kinematics model……Page 219
5.1. Interpolation using quaternions……Page 220
5.2. Spherical linear interpolation……Page 221
5.3. The numerical problem in ocasion of smal values of……Page 222
References……Page 223
The existence of indefinite metrics of signature (++–) and two kinds of almost complex structures in dimension four Y. Matsushita……Page 225
References……Page 240
1. Introduction……Page 242
2. The asymptotic reductions of (1.1)……Page 244
3. The WKB approximations……Page 247
4. Formal computation of matching matrices……Page 250
5. Matching matrices for (1.1)……Page 256
References……Page 257
1. Introduction……Page 259
2. Bezier spline curves in a Euclidean space……Page 260
3. Rational BQzier spline curves on a Euclidean plane……Page 262
4. Projective BQzier spline curves on a standard sphere……Page 267
5. Projective BQzier spline curves on a hyperbolic plane……Page 269
References……Page 270
1. Introduction……Page 272
3. A frame with two equilibrium shapes……Page 275
4. Analysis of the catastrophe phenomenon of a soap film……Page 280
References……Page 284
Einleitung……Page 285
1. Vorbereitungen……Page 287
2. Parametrische Familien von “Bewegungungen” . Allgemeine Bewegungsablaufe……Page 292
3. Bewegungsablaufe und lokal integrable Felder auf Raumen……Page 298
4. Gleitgleitkinematik, kinematische Unterraume……Page 303
5. Geodatische Kinematik in Zahlenraumen Rn……Page 311
Literatur……Page 316
1. Introduction……Page 319
2. Orbit diagrams……Page 320
3. Delayed logistic map……Page 322
4. Sudden break-up of limit cycles……Page 324
References……Page 329
1. Introduction……Page 331
2. Reflective submanifolds in Riemannian symmetric spaces……Page 332
3. Integration on semi-Riemannian manifolds……Page 333
4. Crofton formulae by reflective submanifolds……Page 334
5. Complex space forms……Page 335
6. Hypersurfaces……Page 338
References……Page 339
1. Introduction……Page 341
2. Preliminaries……Page 342
3. Curvature properties of W1-manifolds……Page 345
4. The Yano connection on almost complex manifolds with Norden metric……Page 347
References……Page 350
1. Classes of almost Hermitian manifolds……Page 351
2. Integrability of almost hyperhermitian manifolds……Page 353
3. 4-dimensional almost hyperhermitian manifolds……Page 354
References……Page 358