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The Resource Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource)
Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource)
Resource Information
The item Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 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) finitedimensional 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 higherorder fibered mechanics. The book chapters include:  foundations of jet bundles and analysis of differential forms and vector fields on jet bundles,  the theory of higherorder 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
 Language

 eng
 eng
 Edition
 1st ed. 2015.
 Extent
 1 online resource (366 p.)
 Note
 Description based upon print version of record
 Contents

 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
 Isbn
 9789462390737
 Label
 Introduction to Global Variational Geometry
 Title
 Introduction to Global Variational Geometry
 Statement of responsibility
 by Demeter Krupka
 Language

 eng
 eng
 Summary
 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) finitedimensional 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 higherorder fibered mechanics. The book chapters include:  foundations of jet bundles and analysis of differential forms and vector fields on jet bundles,  the theory of higherorder 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
 http://library.link/vocab/creatorName
 Krupka, Demeter
 Dewey number

 510
 514.74
 515.64
 516.36
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 fOz4ZJ9zeOk
 Language note
 English
 LC call number
 QA614614.97
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Atlantis Studies in Variational Geometry,
 Series volume
 1
 http://library.link/vocab/subjectName

 Global analysis
 Global differential geometry
 Mathematical optimization
 Global Analysis and Analysis on Manifolds
 Differential Geometry
 Calculus of Variations and Optimal Control; Optimization
 Theoretical, Mathematical and Computational Physics
 Classical and Quantum Gravitation, Relativity Theory
 Label
 Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 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
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 1 online resource (366 p.)
 Form of item
 online
 Isbn
 9789462390737
 Media category
 computer
 Media type code
 c
 Other control number
 10.2991/9789462390737
 Specific material designation
 remote
 System control number

 (CKB)3710000000337934
 (EBL)1967744
 (OCoLC)900193753
 (SSID)ssj0001424509
 (PQKBManifestationID)11801998
 (PQKBTitleCode)TC0001424509
 (PQKBWorkID)11363156
 (PQKB)11237474
 (DEHe213)9789462390737
 (MiAaPQ)EBC1967744
 (EXLCZ)993710000000337934
 Label
 Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 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
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 1 online resource (366 p.)
 Form of item
 online
 Isbn
 9789462390737
 Media category
 computer
 Media type code
 c
 Other control number
 10.2991/9789462390737
 Specific material designation
 remote
 System control number

 (CKB)3710000000337934
 (EBL)1967744
 (OCoLC)900193753
 (SSID)ssj0001424509
 (PQKBManifestationID)11801998
 (PQKBTitleCode)TC0001424509
 (PQKBWorkID)11363156
 (PQKB)11237474
 (DEHe213)9789462390737
 (MiAaPQ)EBC1967744
 (EXLCZ)993710000000337934
Subject
 Calculus of Variations and Optimal Control; Optimization
 Classical and Quantum Gravitation, Relativity Theory
 Differential Geometry
 Global Analysis and Analysis on Manifolds
 Global analysis
 Global differential geometry
 Mathematical optimization
 Theoretical, Mathematical and Computational Physics
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/IntroductiontoGlobalVariationalGeometryby/qAEkOvTRel0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/IntroductiontoGlobalVariationalGeometryby/qAEkOvTRel0/">Introduction to Global Variational Geometry, by Demeter Krupka, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>