Differential Geometry of Spray and Finsler Spaces

ISBN-13: 9789048156733 / Angielski / Miękka / 2010 / 258 str.

Zhongmin Shen

Opis

This book is a comprehensive report of recent developments in Finsler geometry and Spray geometry. Riemannian geometry and pseudo-Riemannian geometry are treated as the special case of Finsler geometry. The geometric methods developed in this subject are useful for studying some problems arising from biology, physics, and other fields. Audience: The book will be of interest to graduate students and mathematicians in geometry who wish to go beyond the Riemannian world. Scientists in nature sciences will find the geometric methods presented useful.

Spis treści

Introduction. 1. Minkowski Spaces. 2. Finsler Spaces. 3. SODEs and Variational Problems. 4. Spray Spaces. 5. S-Curvature. 6. Non-Riemannian Quantities. 7. Connections. 8. Riemann Curvature. 9. Structure Equations of Sprays. 10. Structure Equations of Finsler Metrics. 11. Finsler Spaces of Scalar Curvature. 12. Projective Geometry. 13. Douglas Curvature and Weyl Curvature. 14. Exponential Maps. Bibliography. Index.