| 书目名称 | Introduction to Global Variational Geometry |
| 编辑 | Demeter Krupka |
| 视频video | |
| 概述 | Systematic exposition of the higher-order global variational theory on fibered spaces with complete proofs of basic results.First systematic treatment of variational calculus and its applications for |
| 丛书名称 | Atlantis Studies in Variational Geometry |
| 图书封面 |  |
| 描述 | The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational sequence theory and its consequences for the global inverse problem (cohomology conditions)- examples of variational functionals of mathematical physics. Complete formulations an |
| 出版日期 | Book 2015 |
| 关键词 | conservation law; inverse problem; jet manifold; variational sequence; variational theory |
| 版次 | 1 |
| doi | https://doi.org/10.2991/978-94-6239-073-7 |
| isbn_ebook | 978-94-6239-073-7Series ISSN 2214-0700 Series E-ISSN 2214-0719 |
| issn_series | 2214-0700 |
| copyright | Atlantis Press and the author 2015 |
发表于 2025-3-21 16:28:49
