The Geometry of Lagrange Spaces: Theory and Applications /
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 smoo...
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| Format: | eBook |
| Language: | English |
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Dordrecht :
Springer Netherlands : Imprint : Springer,
1994.
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| Series: | Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application ; ;
59. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. <br/> 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. <br/> For mathematical physicists and applied mathematicians interested in the theory and applications of differential-geometric methods. <br/> |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (304 pages) |
| ISBN: | 9789401107884 (electronic bk.) 9401107882 (electronic bk.) |