Contemporary Mathematics 1996; 310 pp; softcover Volume: 196 ISBN10: 082180507X ISBN13: 9780821805077 List Price: US$74 Member Price: US$59.20 Order Code: CONM/196
 This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by S.S. Chern and cochaired 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 sections3 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 GaussBonnet 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 pseudogroup isomorphism between control systems and certain generalized Finsler structures
 G. Wilkens  Finsler geometry in lowdimensional 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
