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Lectures on Finsler geometry. (English) Zbl 0974.53002
Singapore: World Scientific. xiv, 307 p. (2001).
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.

53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
53C20 Global Riemannian geometry, including pinching