Handbook of Finsler Geometry, 2003

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.

From the reviews:"Finsler geometry is the most general among those geometries which satisfy certain highly natural conditions. ... In the last fifty years many papers and more books appeared on Finsler geometry. So it became difficult to obtain a good overlook on the subject. The present Handbook aims to fill this gap. ... The authors wrote well understandable parts. So the book is easily readable also with little knowledge on Finsler geometry." (Lajos Tamássy, Zentralblatt MATH, Vol. 1057 (8), 2005)