國立虎尾科技大學 |

Introduction to Global Variational Geometry

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to Global Variational Geometry/ by Demeter Krupka.
作者:	Krupka, Demeter.
面頁冊數:	XVII, 354 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Global analysis (Mathematics). -
電子資源:	https://doi.org/10.2991/978-94-6239-073-7
ISBN:	9789462390737

Introduction to Global Variational Geometry
Krupka, Demeter.

Introduction to Global Variational Geometry[electronic resource] /by Demeter Krupka. - 1st ed. 2015. - XVII, 354 p.online resource. - Atlantis Studies in Variational Geometry,12214-0700 ;. - Atlantis Studies in Variational Geometry,2.

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

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

1255807
Global analysis (Mathematics).

LC Class. No.: QA614-614.97

Dewey Class. No.: 514.74

Introduction to Global Variational Geometry
LDR:02935nam a22003975i 4500 001 969436
003 DE-He213
005 20200702040221.0
007 cr nn 008mamaa
008 201211s2015 fr | s |||| 0|eng d
020 $a 9789462390737 $9 978-94-6239-073-7
024 7 $a 10.2991/978-94-6239-073-7 $2 doi
035 $a 978-94-6239-073-7
050 4 $a QA614-614.97
072 7 $a PBKS $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 514.74 $2 23
100 1 $a Krupka, Demeter. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1065997
245 1 0 $a Introduction to Global Variational Geometry $h [electronic resource] / $c by Demeter Krupka.
250 $a 1st ed. 2015.
264 1 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2015.
300 $a XVII, 354 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Atlantis Studies in Variational Geometry, $x 2214-0700 ; $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 analysis (Mathematics). $3 1255807
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Differential geometry. $3 882213
650 0 $a Calculus of variations. $3 527927
650 0 $a Mathematical physics. $3 527831
650 0 $a Gravitation. $3 591793
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 768900
650 2 4 $a Classical and Quantum Gravitation, Relativity Theory. $3 769093
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789462390744
776 0 8 $i Printed edition: $z 9789462390720
830 0 $a Atlantis Studies in Variational Geometry, $x 2214-0700 ; $v 2 $3 1256049
856 4 0 $u https://doi.org/10.2991/978-94-6239-073-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)