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:	9789048146567
Publisher:	Springer Netherlands
Publication date:	12/08/2010
Series:	Fundamental Theories of Physics , #76
Edition description:	Softcover reprint of hardcover 1st ed. 1996
Pages:	280
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

On Deflection Tensor Field in Lagrange Geometrics.- The Differential Geometry of Lagrangians which Generate Sprays.- Partial Nondegenerate Finsler Spaces.- Randers and Kropina Spaces in Geodesic Correspondence.- Deviations of Geodesics in the Fibered Finslerian Approach.- Sasakian Structures on Finsler Manifolds.- A New Class of Spray-Generating Lagranians.- Some Remarks on Automorphisms of Finsler Bundles.- On Construction of Landsbergian Characteristic Subalgebra.- Conservation Laws of Dynamical Systems via Lagrangians of Second Degree.- General Randers Spaces.- Conservation Laws Associated to Some Dynamical Systems.- Biodynamic Systems and Conservation Laws. Applications to Neuronal Systems.- Computational Methods in Lagrange Geometry.- Phase Portraits and Critical Elements of Magnetic Fields Generated by a Piecewise Rectilinear Electric Circuit.- Killing Equations in Tangent Bundle.- Lebesgue Measure and Regular Mappings in Finsler Spaces.- On a Finsler Metric Derived from Ecology.- A Moor’s Tensorial Integration in Generalized Lagrange Spaces.- The Lagrange Formalism Used in the Modelling of “Finite Range” Gravity.- On the Quantization of the Complex Scalar Fields in S3xR Space-Time.- Nearly Autoparallel Maps of Lagrange and Finsler Spaces.- Applications of Lagrange Spaces to Physics.- On the Differential Geometry of Nonlocalized Field Theory: Poincaré Gravity.

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