大葉大學圖書館 |

Introduction to global variational geometry[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	516.362
書名/作者:	Introduction to global variational geometry/ by Demeter Krupka.
作者:	Krupka, Demeter.
出版者:	Paris : : Atlantis Press :, 2015.
面頁冊數:	xvii, 354 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Global differential geometry.
標題:	Mathematics.
標題:	Global Analysis and Analysis on Manifolds.
標題:	Differential Geometry.
標題:	Calculus of Variations and Optimal Control; Optimization.
標題:	Theoretical, Mathematical and Computational Physics.
標題:	Classical and Quantum Gravitation, Relativity Theory.
ISBN:	9789462390737 (electronic bk.)
ISBN:	9789462390720 (paper)
內容註:	Jet prolongations of fibred manifolds -- Differential forms on jet prolongations of fibred manifolds -- Formal divergence equations -- Variational structures -- Invariant variational structures -- Examples: Natural Lagrange structures -- Elementary sheaf theory -- Variational sequences.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.2991/978-94-6239-073-7

Introduction to global variational geometry[electronic resource] /
Krupka, Demeter.

Introduction to global variational geometry[electronic resource] /by Demeter Krupka. - Paris :Atlantis Press :2015. - xvii, 354 p. :ill., digital ;24 cm. - Atlantis studies in variational geometry,v.12214-0700 ;. - Atlantis studies in variational geometry ;v.1..

Jet prolongations of fibred manifolds -- Differential forms on jet prolongations of fibred manifolds -- Formal divergence equations -- Variational structures -- Invariant variational structures -- Examples: Natural Lagrange structures -- Elementary sheaf theory -- Variational sequences.

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.

ISBN: 9789462390737 (electronic bk.)

Standard No.: 10.2991/978-94-6239-073-7doiSubjects--Topical Terms:

444409
Global differential geometry.

LC Class. No.: QA670

Dewey Class. No.: 516.362

Introduction to global variational geometry[electronic resource] /
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