Handbook of Finsler geometry. 1 (2003)

Front Cover
Peter L. Antonelli
Springer Science & Business Media, 2003 - Mathematics - 1437 pages
1 Review
There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry). After studying either one of these, the reader will be able to understand the included survey articles on complex manifolds, holonomy, sprays and KCC-theory, symplectic structures, Legendre duality, Hodge theory and Gauss-Bonnet formulas. Finslerian diffusion theory is presented by its founders, P. Antonelli and T. Zastawniak. To help with calculations and conceptualizations, a CD-ROM containing the software package FINSLER, based on MAPLE, is included with the book.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Finsler Metrics 1347
7
Kahler Fibrations
9
Complex Finsler Bundles
23
Kobayashi Metrics
59
The Geometry of Lagrange Spaces 969
89
The Geometry of the Tangent Bundle
91
Nonlinear Connections
97
Finsler Connections on the Tangent Bundle
109
Appendix A Diffusion and Laplacian on the Base Space
335
Appendix B TwoDimensional Constant Berwald Spaces
343
The Geometry of TM and TM
363
Symplectic Transformations of the Differential Geometry
385
The Duality Between Lagrange and Hamilton Spaces
413
Symbolic Finsler Geometry 1125
449
Holonomy of Positively Homogeneous Connections
453
Holonomies of Finsler V Connections
463

Connection
112
Parallelism
116
Second Order Differential Equations
123
Homogeneous Systems of Second Order Differential
135
The Classical Projective Geometry of Paths
151
Normal Spray Connection
161
Lagrange Spaces 1013
173
Finsler Spaces
187
Introduction to Stochastic Calculus on Manifolds
213
Stochastic Development on Finsler Spaces
227
VolterraHamilton Systems of Finsler Type
249
Finslerian Diffusion and Curvature
295
Diffusion on the Tangent and Indicatrix Bundles
319
Holonomies of the Finsler Vector Bundle
469
Holonomies of Special Finsler Manifolds
477
Topological Preliminary
497
The Correction Term
503
Differential Operators 1191
515
Modules and Exact Sequences 1403
517
Elliptic Complexes
521
The Weitzenbock Formula
533
Finsler Metrics
565
Connections in Finsler Spaces
601
Important Finsler Spaces
677
Copyright

Common terms and phrases

Popular passages

Page 485 - Scalar and gradient vector fields of Finsler spaces and holonomy groups of nonlinear connection, Demonst.
Page 485 - PANDE, KS, 1970. On the Finsler space admitting a holonomy group. Ann. Mat. Pura Appl. (IV) 85, 327-346.

Bibliographic information