Geometric Vector Fields of Spray and Metric Structures: Basic Notions, Theorems and Examples

Finsler geometry has been a main field of differential geometry in the 20th and 21st century. Its most natural generalizations are spray geometry and the geometry of generalized metric (Riemannian) spaces. This volume contains the author's own results embedded in the solid framework of classical results. Wherever possible, the author uses a modern, index- and coordinate-free apparatus. An Appendix, however, contains the formulations of several geometric objects presented in the text in terms of coordinates as well. The author quotes the most important original sources as well as the treatises recommendable for further reading. The book is reasonably self-contained and gives an overview of the state of the art of spray and metric structures. Thus it may be useful to read it also as a comprehensive yet brief introduction to the field. The prerequisites that are necessary for the reading of this book do not exceed the knowledge of the fundamental notions related to differentiable manifolds, i.e., no previous knowledge of Finsler or spray geometry is required.