Lectures on Finsler geometry (Q2732569)

This book is intended to provide basic material for Finsler geometry including Riemannian geometry. In particular, the first four chapters cover basics on regular metrics and regular measures on manifolds. In the next chapters, the author introduces the notions of geodesics, of Chern connection, various non-Riemann quantities with their geometric meanings, and he studies metric properties of Finsler spaces, geometric structure of Finsler spaces and Finsler \(m\) spaces. Moreover, he applies Morse theory to the canonical energy functional on the loop space. Finally, in the last chapter, the author considers a Finsler space as a point of a space of Finsler spaces equipped with the Gromov-Hausdorff distance.