A Sampler of Riemann-Finsler Geometry

by David Bao, Robert L. Bryant, Shiing-Shen Chern, Zhongmin Shen

Overview

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.

Product Details

ISBN-13:	9780521831819
Publisher:	Cambridge University Press
Publication date:	11/01/2004
Series:	Mathematical Sciences Research Institute Publications , #50
Pages:	376
Product dimensions:	6.14(w) x 9.21(h) x 0.87(d)

Table of Contents

Preface; Synopses; 1. Volumes on normed and Finsler spaces J. C. Álverez Paiva and A. C. Thompson; 2. Anisotropic and crystalline mean curvature flow Giovanni Bellettini; 3. Finsler geometry on complex vector bundles Tadashi Aikou; 4. Finsler geometry of holomorphic jet bundles Karen Chandler and Pit-Mann Wong; 5. Ricci and flag curvatures in Finsler geometry David Bao and Colleen Robles; 6. Nonreversible Finsler metrics of positive flag curvature Hans-Bert Rademacher; 7. Landsberg curvature, S-curvature and Riemann curvature Zhongmin Shen; Index.