Differential Geometry of Spray and Finsler Spaces

Abstract

This book is the outcome of Shen's endeavor to understand the geometry embodied in systems of second-order ordinary differential equations, and projective Finsler geometry. The author has sorted through a plethora of literature, including many of his own papers, to arrive at the account presented in the book. There is an enormous variety of examples to illustrate the concepts introduced. Also, the author does not restrict his discussions to the positive definite case; hence the book should prove useful to a wide readership. Finally, it is clear that Ludwig Berwald is one of the author's heroes, and rightfully so. A very brief synopsis of Berwald's life is included in the book. For those who would like to read more about Berwald, the source of that synopsis is the long obituary/tribute written by Max Pinl (and translated by P. Bergmann and M. Grumet) in refScripta Math. 27 (1964), 193-203; MR0179051 (31 3302). Reviewed by David Bao