Finsler Geometry Relativity and Gauge Theories

Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to ...

Finsler Geometry  Relativity and Gauge Theories

The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian geometry justify the attempt to systematize the basic techniques for extending general relativity on the basis of Finsler geometry. It is this endeavour that forms the subject matter of the present book. Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to elucidate in this book. The book has been written in such a way that the reader acquainted with the methods of tensor calculus and linear algebra at the graduate level can use it as a manual of Finslerian techniques orientable to applications in several fields. The problems attached to the chapters are also intended to serve this purpose. This notwithstanding, whenever we touch upon the Finslerian refinement or generalization of physical concepts, we assume that the reader is acquainted with these concepts at least at the level of the standard textbooks, to which we refer him or her.

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Finsler Geometry, Relativity and Gauge Theories
Language: en
Pages: 370
Authors: G.S. Asanov
Categories: Science
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian
Handbook of Finsler geometry. 2 (2003)
Language: en
Pages: 1437
Authors: Peter L. Antonelli
Categories: Mathematics
Type: BOOK - Published: 2003 - Publisher: Springer Science & Business Media

There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange
Lagrange and Finsler Geometry
Language: en
Pages: 280
Authors: P.L. Antonelli, R. Miron
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

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
The Geometry of Lagrange Spaces: Theory and Applications
Language: en
Pages: 289
Authors: R. Miron, Mihai Anastasiei
Categories: Science
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Differential-geometric methods are gaining increasing importance in the understanding of a wide range of fundamental natural phenomena. Very often, the starting point for such studies is a variational problem formulated for a convenient Lagrangian. From a formal point of view, a Lagrangian is a smooth real function defined on the
An Introduction to Riemann-Finsler Geometry
Language: en
Pages: 435
Authors: D. Bao, S.-S. Chern, Z. Shen
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.