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.
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978-0-8218-0507-7 (9780821805077)
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Schweitzer Klassifikation
Section 1. Finsler Geometry over the Reals: On the Gauss-Bonnet integrand for $4$-dimensional Landsberg spaces by D. Bao, S. Chern, and Z. Shen Finsler structures on the $2$-sphere satisfying $K = 1$ by R. Bryant Integral geometry in Minkowski spaces by G. D. Chakerian Riemannian geometry as a special case of Finsler geometry by S. Chern Dirac operators for Finsler spaces by F. J. Flaherty Special eigenforms on the sphere bundle of a Finsler manifold by D. Bao and B. Lackey Remarks on Berwald and Landsberg spaces by M. Matsumoto Finsler manifolds of constant positive curvature by Z. Shen Section 2. Complex Finsler Geometry: Finsler metrics of constant curvature and the characterization of tube domains by M. Abate and G. Patrizio Some remarks on locally conformal complex Berwald spaces by T. Aikou Variations of holomorphic curvature for Kahler Finsler metrics by J. Bland and M. Kalka The equivalence problem for complex Finsler Hamiltonians by J. Faran Complex Finsler vector bundles by S. Kobayashi Section 3. Generalized Finsler Metrics: Certain generalizations of Finsler metrics by M. Anastasiei A historical remark on the connections of Chern and Rund by M. Anastasiei On Landsberg spaces and holonomy of Finsler manifolds by L. Kozma Some problems in the geometries of Finsler type by R. Miron Section 4. Applications to Biology, Engineering, and Physics: On $y$-Berwald spaces of dimension two and associated heterochronic systems with Finslerian noise by P. Antonelli, M. Matsumoto, and T. Zastawniak On physical applications of Finsler geometry by R. Ingarden Section 5. Applications to Control Theory: A pseudo-group isomorphism between control systems and certain generalized Finsler structures by R. Gardner and G. Wilkens Finsler geometry in low-dimensional control theory by G. Wilkens Section 6. Applications to Relativistic Field Theory: Finsler geometry and a unified field theory by R. Beil Finslerian spacetime by H. Brandt Symmetry in Finsler spaces by S. Rutz Elementary geometries underlying the theory of Euclidean connections on Finsler metrics of Lorentzian signature by J. Vargas and D. Torr.
