Ebook: An introduction to differentiable manifolds and Riemannian geometry

Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. This book presents an expository account of seven important topics in Riemann-Finsler geometry, ones which have recently undergone significant development but have not had a detailed pedagogical treatment elsewhere. Each article will open the door to an active area of research, and is suitable for a special topics course in graduate-level differential geometry. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry, and parametrized jet bundles, and include a variety of instructive examples Introduction to Manifolds; Functions of Several Variables and Mappings; Differentiable Manifolds and Submanifolds; Vector Fields on a Manifold; Tensors and Tensor Fields on Manifolds; Integration on Manifolds; Differentiation on Riemannian Manifolds; Curvature; Index