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 ManifoldsFinsler MetricsConnections and CurvaturesS-CurvatureRiemann CurvatureFurther Studies:Projective ChangesComparison TheoremsFundamental Groups of Finsler ManifoldsMinimal Immersions and Harmonic MapsEinstein MetricsMiscellaneous TopicsAppendix: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 geometryThis book is written based on several years of teaching experienceIt is so far the most comprehensive book on Finsler geometryFinsler geometry develops rapidly, especially in China. It includes recent results for further studies where many of these results are obtained by young Chinese mathematicians