INTRODUCTION TO MODERN FINSLER GEOMETRY

This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.

In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.

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Contents:

• Foundations:
  • Differentiable Manifolds
  • Finsler Metrics
  • Connections and Curvatures
  • S-Curvature
  • Riemann Curvature
• Further Studies:
  • Projective Changes
  • Comparison Theorems
  • Fundamental Groups of Finsler Manifolds
  • Minimal Immersions and Harmonic Maps
  • Einstein Metrics
  • Miscellaneous Topics
• Appendix:
  • Maple Program

Readership: Graduates and researchers interested in Finsler geometry.
Finsler Metrics;Chern Connection;Ricci Curvature;Riemann Curvature;Flag Curvature;Non-Riemannian Quantity;Comparison Theorem;Fundamental Group;Minimal Immersion;Harmonic Map;Einstein Metric;Projective Transformation;Conformal TransformationKey Features:

• This book is for the beginner as well as researchers who are interested in Finsler geometry
• This book is written based on several years of teaching experience
• It is so far the most comprehensive book on Finsler geometry
• Finsler geometry develops rapidly, especially in China. It includes recent results for further studies where many of these results are obtained by young Chinese mathematicians