A Sampler of Riemann-Finsler Geometry

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

• ISBN13: 9780521831819
• ISBN10: 0521831814
• Format: Hardcover
• Copyright: 2004-11-01
• Publisher: Cambridge University Press

Summary

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 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 parametrised jet bundles, and include a variety of instructive examples.

Table of Contents

Preface	ix
Synopses	xi
Volumes on Normed and Finsler Spaces	1	(48)
J. C. Alvarez Paiva
A. C. Thompson
Anisotropic and Crystalline Mean Curvature Flow	49	(34)
Giovanni Bellettini
Finsler Geometry on Complex Vector Bundles	83	(24)
Tadashi Aikou
Finsler Geometry of Holomorphic Jet Bundles	107	(90)
Karen Chandler
Pit-Mann Wong
Ricci and Flag Curvatures in Finsler Geometry	197	(64)
David Bao
Colleen Robles
Nonreversible Finsler Metrics of Positive Flag Curvature	261	(42)
Hans-Bert Rademacher
Landsberg Curvature, S-Curvature and Riemann Curvature	303	(54)
Zhongmin Shen
Index	357