A Sampler of Riemann-Finsler Geometry (Mathematical Sciences Research Institute Publications, Series Number 50)

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 Seven Important Topics In Riemann-finsler Geometry, 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.--jacket. Volumes On Normed And Finsler Spaces / J.c. Alvarez Paiva And A.c. Thompson -- Anisotropic And Crystalline Mean Curvature Flow / Giovanni Bellettini -- Finsler Geometry On Complex Vector Bundles / Tadashi Aikou -- Finsler Geometry Of Holomorphic Jet Bundles / Karen Chandler And Pit-mann Wong -- Ricci And Flag Curvatures In Finsler Geometry / David Bao And Colleen Robles -- Nonreversible Finsler Metrics Of Positive Flag Curvature / Hans-bert Rademacher -- Landsberg Curvature, S-curvature And Riemann Curvature / Zhongmin Shen. Edited By David Bao ... [et Al.]. Includes Bibliographical References And Index. Cover......Page 1 Summary......Page 2 Mathematical Sciences Research Institute Publications 50......Page 4 A Sampler of Riemann{Finsler Geometry......Page 6 ISBN 9780521831819......Page 7 Contents......Page 8 Preface......Page 10 Synopses......Page 12 Volumes on Normed and Finsler Spaces......Page 15 Anisotropic and Crystalline Mean Curvature Flow......Page 63 Finsler Geometry on Complex Vector Bundles......Page 97 Finsler Geometry of Holomorphic Jet Bundles......Page 121 Ricci and Flag Curvatures in Finsler Geometry......Page 211 Nonreversible Finsler Metrics of Positive Flag Curvature......Page 275 Landsberg Curvature, S-Curvature and Riemann Curvature......Page 317 Index......Page 371 Volumes on normed and Finsler spaces / J.C. Álvarez Paiva and A.C. Thompson Anisotropic and crystalline mean curvature flow / Giovanni Bellettini Finsler geometry on complex vector bundles / Tadashi Aikou Finsler geometry of holomorphic jet bundles / Karen Chandler and Pit-Mann Wong Ricci and flag curvatures in Finsler geometry / David Bao and Colleen Robles Nonreversible Finsler metrics of positive flag curvature / Hans-Bert Rademacher Landsberg curvature, S-curvature and Riemann curvature / Zhongmin Shen 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. The study of volumes and areas on normed and Finsler spaces is a relatively new field that comprises and unifies large domains of convexity, geometric tomography, and integral geometry. These expository accounts treat issues related to volume, geodesics, curvature and mathematical biology, with instructive examples.