Lagrange and Finsler Geometry: Applications to Physics and Biology

by P.L. Antonelli (Editor), R. Miron (Editor)

Overview

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 -Lagrange manifolds, electromagnetic theory and neurophysiology.
Audience: 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.

Product Details

ISBN-13:	9780792338734
Publisher:	Springer Netherlands
Publication date:	12/31/1995
Series:	Fundamental Theories of Physics , #76
Edition description:	1996
Pages:	280
Product dimensions:	6.14(w) x 9.21(h) x 0.03(d)

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. Bácsó. 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. Kovács. 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: Poincaré Gravity; P.C. Stavrinos, P. Manouselis.

Editorial Reviews

‘ ... 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)

From the Publisher