Finslerian Geometries

1. Front Matter

   Pages i-viii

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2. Pedagogy

   1. Front Matter

      Pages 1-1

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   2. Generalizations of Finsler Geometry

      • M. Anastasiei, D. Hrimiuc

      Pages 3-7

   3. Finsler Geometry Inspired

      • L. Kozma, L. Tamássy

      Pages 9-14

   4. Finsler Geometry

      • Hideo Shimada, Vasile Sorin SabĂu

      Pages 15-24

3. Summary and Overview

   1. Front Matter

      Pages 25-25

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   2. Summary and Overview

      • P. L. Antonelli

      Pages 27-32

4. Meeting of Minds

   1. Front Matter

      Pages 33-33

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   2. Some Remarks on the Conformal Equivalence of Complex Finsler Structures

      • Tadashi Aikou

      Pages 35-52

   3. Deformations of Finsler Metrics

      • Mihai Anastasiei, Hideo Shimada

      Pages 53-65

   4. The Constant Sprays of Classical Ecology and Their Noisy Perturbations

      • P. L. Antonelli

      Pages 67-77

   5. On the Geometry of a Homogeneous Contact Transformation

      • P. L. Antonelli, D. Hrimiuc

      Pages 79-87

   6. On Finsler Spaces of Douglas Type III

      • S. Bácsó, M. Matsumoto

      Pages 89-94

   7. Equations of Motion from Finsler Geometric Methods

      • R. G. Beil

      Pages 95-109

   8. On the Theory of Finsler Submanifolds

      • Aurel Bejancu

      Pages 111-129

   9. Finslerian Fields

      • Howard E. Brandt

      Pages 131-138

   10. On the Inverse Problem of the Calculus of Variations for Systems of Second-Order Ordinary Differential Equations

       • M. Crampin

       Pages 139-149

   11. Complex Finsler Geometry Via the Equivalence Problem on the Tangent Bundle

       • James J. Faran V

       Pages 151-168

   12. Lévy Concentration of Metric Measure Manifolds

       • Weiqing Gu, Zhongmin Shen

       Pages 169-177

   13. Hypersurfaces in Generalized Lagrange Spaces

       • Masashi Kitayama

       Pages 179-191

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.

• Area
• Finsler geometry
• Volume
• differential geometry
• ecology
• manifold
• optimization

`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)

• Department of Mathematical Sciences, University of Alberta, Edmonton, Canada

  P. L. Antonelli

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