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Finsler Geometry
Edited by: David Bao, University of Houston, TX, Shiing-shen Chern, University of California, Berkeley, CA, and Zhongmin Shen, Indiana-Purdue University at Indianapolis, IN
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Contemporary Mathematics
1996; 310 pp; softcover
Volume: 196
ISBN-10: 0-8218-0507-X
ISBN-13: 978-0-8218-0507-7
List Price: US$74
Member Price: US$59.20
Order Code: CONM/196
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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

Section 1. Finsler Geometry over the Reals
  • D. Bao, S. Chern, and Z. Shen -- On the Gauss-Bonnet integrand for \(4\)-dimensional Landsberg spaces
  • R. Bryant -- Finsler structures on the \(2\)-sphere satisfying \(K = 1\)
  • G. D. Chakerian -- Integral geometry in Minkowski spaces
  • S. Chern -- Riemannian geometry as a special case of Finsler geometry
  • F. J. Flaherty -- Dirac operators for Finsler spaces
  • D. Bao and B. Lackey -- Special eigenforms on the sphere bundle of a Finsler manifold
  • M. Matsumoto -- Remarks on Berwald and Landsberg spaces
  • Z. Shen -- Finsler manifolds of constant positive curvature
Section 2. Complex Finsler Geometry
  • M. Abate and G. Patrizio -- Finsler metrics of constant curvature and the characterization of tube domains
  • T. Aikou -- Some remarks on locally conformal complex Berwald spaces
  • J. Bland and M. Kalka -- Variations of holomorphic curvature for Kähler Finsler metrics
  • J. Faran -- The equivalence problem for complex Finsler Hamiltonians
  • S. Kobayashi -- Complex Finsler vector bundles
Section 3. Generalized Finsler Metrics
  • M. Anastasiei -- Certain generalizations of Finsler metrics
  • M. Anastasiei -- A historical remark on the connections of Chern and Rund
  • L. Kozma -- On Landsberg spaces and holonomy of Finsler manifolds
  • R. Miron -- Some problems in the geometries of Finsler type
Section 4. Applications to Biology, Engineering, and Physics
  • P. Antonelli, M. Matsumoto, and T. Zastawniak -- On \(y\)-Berwald spaces of dimension two and associated heterochronic systems with Finslerian noise
  • R. Ingarden -- On physical applications of Finsler geometry
Section 5. Applications to Control Theory
  • R. Gardner and G. Wilkens -- A pseudo-group isomorphism between control systems and certain generalized Finsler structures
  • G. Wilkens -- Finsler geometry in low-dimensional control theory
Section 6. Applications to Relativistic Field Theory
  • R. Beil -- Finsler geometry and a unified field theory
  • H. Brandt -- Finslerian spacetime
  • S. Rutz -- Symmetry in Finsler spaces
  • J. Vargas and D. Torr -- Elementary geometries underlying the theory of Euclidean connections on Finsler metrics of Lorentzian signature
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