Introduction to Modern Finsler Geometry

Yi-Bing Shen and Zhongmin Shen present a textbook for graduate and senior undergraduate students on a type of geometry that does not require quadratics. The concept was noted by Riemann as early as 1854, they say, but lay dormant until 1918, when P. Finsler studied the geometry of curves and surfaces in the general case. They cover differentiable manifolds, Finsler metrics, connections and curvatures, S-curvature, Riemann curvature, projective changes, comparison theorems, fundamental groups of Finsler manifolds, minimal immersions and harmonic maps, Einstein metrics, and miscellaneous topics. Annotation c2016 Ringgold, Inc., Portland, OR (protoview.com)