Introduction to Global Variational Geometry
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...
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2015
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57873 |
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oai:scholar.dlu.edu.vn:DLU123456789-578732023-11-11T05:54:58Z Introduction to Global Variational Geometry Krupka, Demeter General Geometry Mathematics Global differential geometry 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 and proofs of all basic assertions are given, based on theorems of global analysis explained in the Appendix. 2015-08-31T09:14:58Z 2015-08-31T09:14:58Z 2015 Book 978-94-6239-073-7 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57873 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
General Geometry Mathematics Global differential geometry |
| spellingShingle |
General Geometry Mathematics Global differential geometry Krupka, Demeter Introduction to Global Variational Geometry |
| description |
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 and proofs of all basic assertions are given, based on theorems of global analysis explained in the Appendix. |
| format |
Book |
| author |
Krupka, Demeter |
| author_facet |
Krupka, Demeter |
| author_sort |
Krupka, Demeter |
| title |
Introduction to Global Variational Geometry |
| title_short |
Introduction to Global Variational Geometry |
| title_full |
Introduction to Global Variational Geometry |
| title_fullStr |
Introduction to Global Variational Geometry |
| title_full_unstemmed |
Introduction to Global Variational Geometry |
| title_sort |
introduction to global variational geometry |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57873 |
| _version_ |
1782535697468489728 |