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010   $a94-6239-073-8
024 7 $a10.2991/978-94-6239-073-7
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035   $a(EBL)1967744
035   $a(OCoLC)900193753
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035   $a(DE-He213)978-94-6239-073-7
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100   $a20150113d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aIntroduction to Global Variational Geometry /$fby Demeter Krupka
205   $a1st ed. 2015.
210  1$aParis :$cAtlantis Press :$cImprint: Atlantis Press,$d2015.
215   $a1 online resource (366 p.)
225 1 $aAtlantis Studies in Variational Geometry,$x2214-0719 ;$v1
300   $aDescription based upon print version of record.
311 08$a94-6239-072-X 
320   $aIncludes bibliographical references and index.
327   $aJet 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.
330   $aThe book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational sequence theory and its consequences for the global inverse problem (cohomology conditions)- examples of variational functionals of mathematical physics. Complete formulations and proofs of all basic assertions are given, based on theorems of global analysis explained in the Appendix.
410  0$aAtlantis Studies in Variational Geometry,$x2214-0719 ;$v1
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aGeometry, Differential
606   $aMathematical optimization
606   $aCalculus of variations
606   $aMathematical physics
606   $aGravitation
606   $aGlobal Analysis and Analysis on Manifolds
606   $aDifferential Geometry
606   $aCalculus of Variations and Optimization
606   $aTheoretical, Mathematical and Computational Physics
606   $aClassical and Quantum Gravity
615  0$aGlobal analysis (Mathematics)
615  0$aManifolds (Mathematics)
615  0$aGeometry, Differential.
615  0$aMathematical optimization.
615  0$aCalculus of variations.
615  0$aMathematical physics.
615  0$aGravitation.
615 14$aGlobal Analysis and Analysis on Manifolds.
615 24$aDifferential Geometry.
615 24$aCalculus of Variations and Optimization.
615 24$aTheoretical, Mathematical and Computational Physics.
615 24$aClassical and Quantum Gravity.
676   $a516.362
700   $aKrupka$b Demeter$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755735
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299761003321
996   $aIntroduction to global variational geometry$91522916
997   $aUNINA