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Miron, Radu; Miron, R.; Anastasiei, M. 作者

译者

1993-11 出版日期

303 页数

$ 270.07 价格

丛书系列

9780792325918 图书编码

The Geometry of Lagrange Spaces 在线电子书图书标签: 数学-辛几何数学-纤维丛数学-微分几何数学

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The Geometry of Lagrange Spaces 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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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.

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