Finsler Geometry, Relativity and Gauge Theories
Finsler Geometry, Relativity and Gauge Theories

Author: G.S. Asanov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 375

ISBN-13: 9400953291

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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.

Finsler Geometry, Relativity and Gauge Theories
Finsler Geometry, Relativity and Gauge Theories

Author: G.S. Asanov

Publisher: Springer

Published: 1985

Total Pages: 392

ISBN-13:

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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.

The Geometry of Lagrange Spaces: Theory and Applications
The Geometry of Lagrange Spaces: Theory and Applications

Author: R. Miron

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 302

ISBN-13: 9401107882

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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 total space of the tangent bundle to a manifold satisfying some regularity conditions. The main purpose of this book is to present: (a) an extensive discussion of the geometry of the total space of a vector bundle; (b) a detailed exposition of Lagrange geometry; and (c) a description of the most important applications. New methods are described for construction geometrical models for applications. The various chapters consider topics such as fibre and vector bundles, the Einstein equations, generalized Einstein--Yang--Mills equations, the geometry of the total space of a tangent bundle, Finsler and Lagrange spaces, relativistic geometrical optics, and the geometry of time-dependent Lagrangians. Prerequisites for using the book are a good foundation in general manifold theory and a general background in geometrical models in physics. For mathematical physicists and applied mathematicians interested in the theory and applications of differential-geometric methods.

Geometry of Pseudo-Finsler Submanifolds
Geometry of Pseudo-Finsler Submanifolds

Author: Aurel Bejancu

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 252

ISBN-13: 9401594171

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This book begins with a new approach to the geometry of pseudo-Finsler manifolds. It also discusses the geometry of pseudo-Finsler manifolds and presents a comparison between the induced and the intrinsic Finsler connections. The Cartan, Berwald, and Rund connections are all investigated. Included also is the study of totally geodesic and other special submanifolds such as curves, surfaces, and hypersurfaces. Audience: The book will be of interest to researchers working on pseudo-Finsler geometry in general, and on pseudo-Finsler submanifolds in particular.

The Geometry of Higher-Order Hamilton Spaces
The Geometry of Higher-Order Hamilton Spaces

Author: R. Miron

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 257

ISBN-13: 9401000700

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This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, 2001). It contains the general theory of higher order Hamilton spaces H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their structure equations, and the Riemannian almost contact metrical model of these spaces. In addition, the volume also describes new developments such as variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law of conservation; Noether symmetries; Hamilton subspaces of order k and their fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the same order is pointed out. Also, the geometry of Cartan spaces of order k =1 is investigated in detail. This theory is useful in the construction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc.

Differential Geometry And Its Applications - International Conference
Differential Geometry And Its Applications - International Conference

Author: Josef Janyska

Publisher: World Scientific

Published: 1990-03-01

Total Pages: 482

ISBN-13: 9814611700

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The proceedings consists of lectures and selected original research papers presented at the conference. The contents is divided into 3 parts: I. Geometric structures, II. the calculus of variations on manifolds, III. Geometric methods in physics. The volume also covers interdisciplinary areas between differential geometry and mathematical physics like field theory, relativity, classical and quantum mechanics.

Global Differential Geometry
Global Differential Geometry

Author: Alfred Gray

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 490

ISBN-13: 0821827502

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Alfred Gray's work covered a great part of differential geometry. In September 2000, a remarkable International Congress on Differential Geometry was held in his memory in Bilbao, Spain. Mathematicians from all over the world, representing 24 countries, attended the event. This volume includes major contributions by well known mathematicians (T. Banchoff, S. Donaldson, H. Ferguson, M. Gromov, N. Hitchin, A. Huckleberry, O. Kowalski, V. Miquel, E. Musso, A. Ros, S. Salamon, L. Vanhecke, P. Wellin and J.A. Wolf), the interesting discussion from the round table moderated by J.-P. Bourguignon, and a carefully selected and refereed selection of the Short Communications presented at the Congress. This book represents the state of the art in modern differential geometry, with some general expositions of some of the more active areas: special Riemannian manifolds, Lie groups and homogeneous spaces, complex structures, symplectic manifolds, geometry of geodesic spheres and tubes and related problems, geometry of surfaces, and computer graphics in differential geometry.

Jingshin Physics Symposium In Memory Of Prof Wolfgang Kroll
Jingshin Physics Symposium In Memory Of Prof Wolfgang Kroll

Author: Jong-ping Hsu

Publisher: World Scientific

Published: 1997-06-13

Total Pages: 426

ISBN-13: 9814546194

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Dr W Kroll, a young post-doc working under Heisenberg at Leipzing in the 1930s, was forced to escape from the Nazis and eventually came to the National Taiwan University in 1941. He taught many of the advanced courses in theoretical physics for over two decades, and prepared a generation of physicists in Taiwan. A symposium on pure and applied physics was held in memory of Prof Kroll at the University of Massachusetts Dartmouth in August 1996. These proceedings, composed of papers contributed to the symposium by many of Prof Kroll's former students now reaching professorial ranks in the West, reflect in a small measure the legacy he left behind.

Geometry, Fields and Cosmology
Geometry, Fields and Cosmology

Author: B.R. Iyer

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 575

ISBN-13: 9401716951

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This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989. This series of Schools have been carefully planned to provide a sound background and preparation for students embarking on research in these and related topics. Consequently, the contents of these lectures have been meticulously selected and arranged. The topics in the present volume offer a firm mathematical foundation for a number of subjects to be de veloped later. These include Geometrical Methods for Physics, Quantum Field Theory Methods and Relativistic Cosmology. The style of the book is pedagogical and should appeal to students and research workers attempt ing to learn the modern techniques involved. A number of specially selected problems with hints and solutions have been included to assist the reader in achieving mastery of the topics. We decided to bring out this volume containing the lecture notes since we felt that they would be useful to a wider community of research workers, many of whom could not participate in the school. We thank all the lecturers for their meticulous lectures, the enthusiasm they brought to the discussions and for kindly writing up their lecture notes. It is a pleasure to thank G. Manjunatha for his meticulous assistence over a long period, in preparing this volume for publication.