A Sampler of Riemann-Finsler Geometry

This book presents expository accounts of six important topics in Finsler geometry suitable for a special-topics graduate course in differential geometry. They treat issues related to volume, geodesics, curvature and mathematical biology, and provide a good variety of instructive examples.

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Finsler geometry generalises Riemannian geometry in the same sense that Banach spaces generalise Hilbert spaces. This book presents an expository account of seven important topics in Riemann–Finsler geometry, ones which have 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 parametrised jet bundles, and include a variety of instructive examples.