Finsler Geometry, Relativity and Gauge Theories, G.S. Asanov

Автор: D. Bao; S.-S. Chern; Z. Shen
Название: An Introduction to Riemann-Finsler Geometry
ISBN: 1461270707 ISBN-13(EAN): 9781461270706
Издательство: Springer
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Описание: In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is natural to wonder just how much geometry one can uncover and describe?
It now appears that there is a reasonable answer. Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature. There is also a bewildering array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. This book focuses on the elementary but essential items among these results. Much thought has gone into making the account a teachable one.

Автор: G.S. Asanov
Название: Finsler Geometry, Relativity and Gauge Theories
ISBN: 9027719608 ISBN-13(EAN): 9789027719607
Издательство: Springer
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Автор: P.L. Antonelli; R. Miron
Название: Lagrange and Finsler Geometry
ISBN: 0792338731 ISBN-13(EAN): 9780792338734
Издательство: Springer
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Описание: The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian. This collection of papers covers higher order Lagrange geometry, the theory of -Lagrange manifolds, electromagnetic theory and neurophysiology.

Автор: Zhongmin Shen
Название: Differential Geometry of Spray and Finsler Spaces
ISBN: 9048156734 ISBN-13(EAN): 9789048156733
Издательство: Springer
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Автор: Shen Yi-Bing Et Al
Название: Introduction To Modern Finsler Geometry
ISBN: 9814704903 ISBN-13(EAN): 9789814704908
Издательство: World Scientific Publishing
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Описание:

This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.

In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.

Автор: P.L. Antonelli; R. Miron
Название: Lagrange and Finsler Geometry
ISBN: 9048146569 ISBN-13(EAN): 9789048146567
Издательство: Springer
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Описание: 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] .

Автор: Hanno Rund
Название: The Differential Geometry of Finsler Spaces
ISBN: 3642516122 ISBN-13(EAN): 9783642516122
Издательство: Springer
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Описание: Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry.

Автор: Shen Yi-Bing Et Al
Название: Introduction To Modern Finsler Geometry
ISBN: 9814713163 ISBN-13(EAN): 9789814713160
Издательство: World Scientific Publishing
Цена: 6336.00 р.
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Описание:

This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.

In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.