**Contemporary Mathematics**

Volume: 196;
1996;
310 pp;
Softcover

MSC: Primary 53;

Print ISBN: 978-0-8218-0507-7

Product Code: CONM/196

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

**Electronic ISBN: 978-0-8218-7787-6
Product Code: CONM/196.E**

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

# Finsler Geometry

Share this page *Edited by *
*David Bao; Shiing-shen Chern; Zhongmin Shen*

This volume features proceedings from the 1995 Joint
Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by
S.S. Chern and co-chaired by D. Bao and Z. Shen.

The editors of this volume have provided comprehensive
and informative “capsules” of presentations and
technical reports. This was facilitated by classifying the papers into
the following 6 separate sections—3 of which are applied and 3
are pure:

- Finsler Geometry over the reals
- Complex Finsler geometry
- Generalized Finsler metrics
- Applications to biology, engineering, and physics
- Applications to control theory
- Applications to relativistic field theory

Each section contains a preface that provides a coherent overview of the topic and includes an outline of the current directions of research and new perspectives. A short list of open problems concludes each contributed paper.

A number of photos are featured in the volume, for example, that of Finsler. In addition, conference participants are also highlighted.

#### Readership

: Graduate students, research mathematicians, physicists, and engineers interested in differential geometry, complex analysis, control theory, and mathematical biology.

# Table of Contents

## Finsler Geometry

- Contents v6 free
- Foreword vii8 free
- Paul Finsler and friends ix10 free
- Section 1: Finsler Geometry over the Reals 126 free
- 0. Preface 328
- 1. On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces 1540
- 2. Finsler structures on the 2-sphere satisfying K = 1 2752
- 3. Integral geometry in Minkowski spaces 4368
- 4. Riemannian geometry as a special case of Finsler geometry 5176
- 5. Dirac operators for Finsler spaces 5984
- 6. Special eigenforms on the sphere bundle of a Finsler manifold 6792
- 7. Remarks on Berwald and Landsberg spaces 79104
- 8. Finsler manifolds of constant positive curvature 83108

- Section 2: Complex Finsler Geometry 95120
- 0. Preface 97122
- 1. Finsler metrics of constant curvature and the characterization of tube domains 101126
- 2. Some remarks on locally conformal complex Berwald spaces 109134
- 3. Variations of holomorphic curvature for Kähler Finsler metrics 121146
- 4. The equivalence problem for complex Finsler Hamiltonians 133158
- 5. Complex Finsler vector bundles 145170

- Section 3: Generalized Finsler Metrics 155180
- Section 4: Applications to Biology, Engineering, and Physics 197222
- Section 5: Applications to Control Theory 225250
- Section 6: Applications to Relativistic Field Theory 259284