Synopses & Reviews
This text will acquaint the reader with the most recent advances in Finslerian geometries, i.e. anisotropic geometries, and their applications by the Japanese, European and American schools. It contains three introductory articles, one from each of these schools, giving a broad overview of basic ideas. Further papers treat topics from pure mathematics such as complex differential geometry, equivalence methods, Finslerian deformations, constant sprays, homogeneous contact transformations, Douglas spaces, submanifold theory, inverse problems, area theory, and more. This book completes the Kluwer trilogy on Finslerian Geometry by P.L. Antonelli and his associates. Audience: This volume will be of interest to physicists and mathematicians whose work involves quantum field theory, combination theory and relativity, programming and optimization. Mathematical biologists working in ecology and evolution will also find it useful.
Review
`aside from being well organized, typesetting of the book as well as proof reading is done very carefully. The layout is professional. The book deserves attention not only from mathematicians but also from natural scientists, especially for theoretical physics. It certainly helps to overcome such judges about Finsler Geometry like `an impenetrable forest whose entire vegetation consists of tenors'or `a jungle of tenors'. This book is highly readable and exciting.' Journal of Geodesy, 75:(5-6)(2001) `It will be of interest to physicist and mathematicians whose work involves quantum field theory, general relativity and gravitation, programming and optimization. Mathematical biologist working in ecology and evolution will also find it useful.' General Relativity and Gravitation, 33:7 (2001) `Aside from being well organized, typesetting of the book as well as proof reading is done very carefully. The layout is professional.. Nevertheless, this book is highly readable and exciting.' Journal of Geodesy, 75:337-342 (2001)
Synopsis
The International Conference on Finsler and Lagrange Geometry and its Applications: A Meeting of Minds, took place August 13-20, 1998 at the University of Alberta in Edmonton, Canada. The main objective of this meeting was to help acquaint North American geometers with the extensive modern literature on Finsler geometry and Lagrange geometry of the Japanese and European schools, each with its own venerable history, on the one hand, and to communicate recent advances in stochastic theory and Hodge theory for Finsler manifolds by the younger North American school, on the other. The intent was to bring together practitioners of these schools of thought in a Canadian venue where there would be ample opportunity to exchange information and have cordial personal interactions. The present set of refereed papers begins -with the Pedagogical Sec- tion I, where introductory and brief survey articles are presented, one from the Japanese School and two from the European School (Romania and Hungary). These have been prepared for non-experts with the intent of explaining basic points of view. The Section III is the main body of work. It is arranged in alphabetical order, by author. Section II gives a brief account of each of these contribu- tions with a short reference list at the end. More extensive references are given in the individual articles.
Table of Contents
Preface. Section I: Pedagogy. Generalizations of Finsler Geometry; M. Anastasiei, D. Hrimiuc. Finsler Geometry Inspired; L. Kozma, L. Tamássy. Finsler Geometry; H. Shimada, V.S. Sabau. Section II: Summary and Overview. Summary and Overview; P.L. Antonelli. Section III: Meeting of Minds. Some Remarks On the Conformal Equivalence of Complex Finsler Structures; T. Aikou. Deformations of Finsler Metrics; M. Anastasiei, H. Shimada. The Constant Sprays of Classical Ecology and Noisy Finsler Perturbations; P.L. Antonelli. On the Geometry of a Homogeneous Contact Transformation; P.L. Antonelli, D. Hrimiuc. On Finsler Spaces of Douglas Type III; S. Bácsó, M. Matsumoto. Equations of Motion from Finsler Geometric Methods; R.G. Beil. On the Theory of Finsler Submanifolds; A. Bejancu. Finslerian Fields; H.E. Brandt. On the Inverse Problem of the Calculus of Variations for Systems of Second-Order Ordinary Differential Equations; M. Crampin. Complex Finsler Geometry Via the Equivalence Problem on the Tangent Bundle; J.J. Faran. Lévy Concentration of Metric Measure Manifolds; W. Gu, Z. Shen. Hypersurfaces in Generalized Lagrange Spaces; M. Kitayama. The Notion of Higher Order Finsler Space. Theory and Applications; R. Miron. Generalized Complex Lagrange Spaces; G. Munteanu. Gravity in Finsler Spaces; S.F. Rutz, F.M. Paiva. Higher Order Ecological Metrics; V.S. Sabau. Area and Metrical Connections in Finsler Space; L. Tamássy. Problem; L. Tamássy. Finslerian Convexity and Optimization; C. Udriste. On Projective Transformations and Conformal Transformations of the Tangent Bundles of Riemannian Manifolds; K. Yamauchi.