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.

This book presents an expository account of six important topics in Riemann-Finsler geometry suitable for in a special topics course in graduate level differential geometry. These topics 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 geometrical research. Rademacher gives a detailed account of his Sphere Theorem for non-reversible Finsler metrics. Alvarez and Thompson present an accessible discussion of the picture which emerges from their search for a satisfactory notion of volume on Finsler manifolds. Wong studies the geometry of holomorphic jet bundles, and finds that Finsler metrics play an essential role. Sabau studies protein production in cells from the Finslerian perspective of path spaces, employing both a local stability analysis of the first order system, and a KCC analysis of the related second order system. Shen's article discusses Finsler metrics whose flag curvature depends on the location and the direction of the flag poles, but not on the remaining features of the flags. Bao and Robles focus on Randers spaces of constant flag curvature or constant Ric