國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Introduction to global variational g...

Krupka, Demeter.

Introduction to global variational geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introduction to global variational geometryby 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.
電子資源:	http://dx.doi.org/10.2991/978-94-6239-073-7
ISBN:	9789462390737 (electronic bk.)

Introduction to global variational geometry
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:

359871
Global differential geometry.

LC Class. No.: QA670

Dewey Class. No.: 516.362

Introduction to global variational geometry
LDR:02591nmm a2200325 a 4500 001 461580
003 DE-He213
005 20150903133605.0
006 m d
007 cr nn 008maaau
008 151110s2015 fr s 0 eng d
020 $a 9789462390737 (electronic bk.)
020 $a 9789462390720 (paper)
024 7 $a 10.2991/978-94-6239-073-7 $2 doi
035 $a 978-94-6239-073-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA670
072 7 $a PBKS $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 516.362 $2 23
090 $a QA670 $b .K94 2015
100 1 $a Krupka, Demeter. $3 713764
245 1 0 $a Introduction to global variational geometry $h [electronic resource] / $c by Demeter Krupka.
260 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2015.
300 $a xvii, 354 p. : $b ill., digital ; $c 24 cm.
490 1 $a Atlantis studies in variational geometry, $x 2214-0700 ; $v v.1
505 0 $a 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.
520 $a 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.
650 0 $a Global differential geometry. $3 359871
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Differential Geometry. $3 273785
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 376743
650 2 4 $a Classical and Quantum Gravitation, Relativity Theory. $3 376367
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Atlantis studies in variational geometry ; $v v.1. $3 713765
856 4 0 $u http://dx.doi.org/10.2991/978-94-6239-073-7
950 $a Mathematics and Statistics (Springer-11649)