Lagrange and Finsler Geometry, P.L. Antonelli; R. Miron

Автор: R. Miron; Dragos Hrimiuc; Hideo Shimada; Sorin V.
Название: The Geometry of Hamilton and Lagrange Spaces
ISBN: 0792369262 ISBN-13(EAN): 9780792369264
Издательство: Springer
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Описание: It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67].

Автор: R. Miron
Название: The Geometry of Higher-Order Lagrange Spaces
ISBN: 079234393X ISBN-13(EAN): 9780792343936
Издательство: Springer
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Цена: 30327.00 р.
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Описание: Devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations, this volume presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. It is suitable for scientists whose work involves differential geometry and mechanics of particles and systems.

Автор: R. Miron
Название: The Geometry of Higher-Order Lagrange Spaces
ISBN: 9048147891 ISBN-13(EAN): 9789048147892
Издательство: Springer
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Цена: 30327.00 р.
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Описание: This monograph is mostly devoted to the problem of the geome- trizing of Lagrangians which depend on higher order accelerations. It naturally prolongs the theme of the monograph "The Geometry of La- grange spaces: Theory and Applications," written together with M. Anastasiei and published by Kluwer Academic Publishers in 1994. The existence of Lagrangians of order k > 1 has been contemplated by mechanicists and physicists for a long time. Einstein had grasped their presence in connection with the Brownian motion. They are also present in relativistic theories based on metrics which depend on speeds and accelerations of particles or in the Hamiltonian formulation of non- linear systems given by Korteweg-de Vries equations. There resulted from here the methods to be adopted in their theoretical treatment. One is based on the variational problem involving the integral action of the Lagrangian. A second one is derived from the axioms of Analytical Mechanics involving the Poincare-Cartan forms. The geometrical methods based on the study of the geometries of higher order could invigorate the whole theory. This is the way adopted by us in defining and studying the Lagrange spaces of higher order. The problems raised by the geometrization of Lagrangians of order k > 1 investigated by many scholars: Ch. Ehresmann, P. Libermann, J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov, P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P. Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo, D.

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: Hanno Rund
Название: The Differential Geometry of Finsler Spaces
ISBN: 3642516122 ISBN-13(EAN): 9783642516122
Издательство: Springer
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Цена: 11179.00 р.
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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.