A Sampler of Riemann-finsler Geometry

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

• ISBN13: 9780521168731
• ISBN10: 0521168732
• Format: Paperback
• Copyright: 2010-09-09
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface

Synopses

Volumes on normed and Finsler spaces

Anisotropic and crystalline mean curvature flow

Finsler geometry on complex vector bundles

Finsler geometry of holomorphic jet bundles

Ricci and flag curvatures in Finsler geometry

Nonreversible Finsler metrics of positive flag curvature

Landsberg curvature, S-curvature and Riemann curvature

Index

Table of Contents provided by Publisher. All Rights Reserved.