Lagrange and Finsler Geometry

Lagrange and Finsler Geometry : Applications to Physics and Biology

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Since 1992 Finsler geometry, Lagrange geometry and their applications to physics and biology, have been intensive1y studied in the context of a 5-year program called "Memorandum ofUnderstanding", between the University of Alberta and "AL.1. CUZA" University in lasi, Romania. The conference, whose proceedings appear in this collection, belongs to that program and aims to provide a forum for an exchange of ideas and information on recent advances in this field. Besides the Canadian and Romanian researchers involved, the conference benefited from the participation of many specialists from Greece, Hungary and Japan. This proceedings is the second publication of our study group. The first was Lagrange Geometry. Finsler spaces and Noise Applied in Biology and Physics (1]. Lagrange geometry, which is concerned with regular Lagrangians not necessarily homogeneous with respect to the rate (i.e. velocities or production) variables, naturalIy extends Finsler geometry to alIow the study of, for example, metrical structures (i.e. energies) which are not homogeneous in these rates. Most Lagrangians arising in physics falI into this class, for example.
Lagrange geometry and its applications in general relativity, unified field theories and re1ativistic optics has been developed mainly by R. Miron and his students and collaborators in Romania, while P. Antonelli and his associates have developed models in ecology, development and evolution and have rigorously laid the foundations ofFinsler diffusion theory [1] .
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Product details

  • Hardback | 280 pages
  • 154.9 x 236.2 x 22.9mm | 544.32g
  • Dordrecht, Netherlands
  • English
  • 1996 ed.
  • X, 280 p.
  • 0792338731
  • 9780792338734

Back cover copy

The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian. Nevertheless, such geometries are playing an increasingly important role in a wide variety of problems in fields ranging from relativistic optics to ecology. The present collection of papers will serve to bring the reader up-to-date on the most recent advances. Subjects treated include higher order Lagrange geometry, the recent theory of (phi)-Lagrange manifolds, electromagnetic theory and neurophysiology. This book is recommended as a (supplementary) text in graduate courses in differential geometry and its applications, and will also be of interest to physicists and mathematical biologists.
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Table of contents

Preface. Part One: Differential Geometry and Applications. On Deflection Tensor Field in Lagrange Geometries; M. Anastasei. The Differential Geometry of Lagrangians which Generate Sprays; M. Anastasiei, P.L. Antonelli. Partial Nondegenerate Finsler Spaces; Gh. Atanasiu. Randers and Kropina Spaces in Geodesic Correspondence; S. Bacso. Deviations of Geodesics in the Fibered Finslerian Approach; V. Balan, P.C. Stavrinos. Sasakian Structures on Finsler Manifolds; I. Hasegawa, et al. A New Class of Spray-Generating Lagrangians; P. Antonelli, D. Hrimiuc. Some Remarks on Automorphisms of Finsler Bundles; M.Sz. Kirkovits, et al. On Construction of Landsbergian Characteristic Subalgebra; Z. Kovacs. Conservation Laws of Dynamical Systems via Lagrangians of Second Degree; V. Marinca. General Randers Spaces; R. Miron. Conservation Laws Associated to Some Dynamical Systems; V. Obadeanu. Biodynamic Systems and Conservation Laws. Applications to Neuronal Systems; V. Obadeanu, V.V. Obadeanu. Computational Methods in Lagrange Geometry; M. Postolache. Phase Portraits and Critical Elements of Magnetic Fields Generated by a Piecewise Rectilinear Electric Circuit; C. Udriste, et al. Killing Equations in Tangent Bundle; M. Yawata. Lebesgue Measure and Regular Mappings in Finsler Spaces; A. Neagu, V.T. Borcea. On a Finsler Metric Derived from Ecology; H. Shimada. Part Two: Geometrical Models in Physics. A Moor's Tensorial Integration in Generalized Lagrange Spaces; I. Gottlieb, S. Vacaru. The Lagrange Formalism Used in the Modelling of `Finite Range' Gravity; I. Ionescu-Pallas, L. Sofonea. On the Quantization of the Complex Scalar Fields in S3xR Space-Time;C. Dariescu, M.-A. Dariescu. Nearly Autoparallel Maps of Lagrange and Finsler Spaces; S. Vacaru, S. Ostaf. Applications of Lagrange Spaces to Physics; Gh. Zet. On the Differential Geometry of Nonlocalized Field Theory: Poincare Gravity; P.C. Stavrinos, P. Manouselis.
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Review quote

` ... good insight into the current state-of-the-art of Finsler and Lagrange geometries. The volume has the following three main audiences: differential geometers, relativists, and workers in Lagrange dynamics. ... can be recommended as a supplementary and more specialized text in the above mentioned topics.'
General Relativity and Gravitation, 29:9 (1997)
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