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Antonelli P.L. Finslerian Geometries: A Meeting of Minds

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Antonelli P.L. Finslerian Geometries: A Meeting of Minds
Amsterdam: Springer, 2000. — 305 p.
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 contribu­tions with a short reference list at the end. More extensive references are given in the individual articles.
Contents :

Front Matter
Front Matter
Generalizations of Finsler Geometry
Finsler Geometry Inspired
Finsler Geometry
Front Matter
Summary and Overview
Front Matter
Some Remarks on the Conformal Equivalence of Complex Finsler Structures
Deformations of Finsler Metrics
The Constant Sprays of Classical Ecology and Their Noisy Perturbations
On the Geometry of a Homogeneous Contact Transformation
On Finsler Spaces of Douglas Type III
Equations of Motion from Finsler Geometric Methods
On the Theory of Finsler Submanifolds
Finslerian Fields
On the Inverse Problem of the Calculus of Variations for Systems of Second-Order Ordinary Differential Equations
Complex Finsler Geometry Via the Equivalence Problem on the Tangent Bundle
Lévy Concentration of Metric Measure Manifolds
Hypersurfaces in Generalized Lagrange Spaces
The Notion of Higher Order Finsler Space. Theory and Applications
Generalized Complex Lagrange Spaces
Gravity in Finsler Spaces
Higher Order Ecological Metrics
Front Matter
Area and Metrical Connections in Finsler Spaces
Finslerian Convexity and Optimization
On Projective Transformations and Conformal Transformations of the Tangent Bundles of Riemannian Manifolds
Back Matter
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