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Introduction to Global Variational Geometry: 1 (Atlantis Studies in Variational Geometry) - Hardcover
Inhaltsangabe
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.
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Reseña del editor
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.
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- VerlagAtlantis Press
- Erscheinungsdatum2015
- ISBN 10 946239072X
- ISBN 13 9789462390720
- EinbandTapa dura
- SpracheEnglisch
- Anzahl der Seiten374
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Introduction to Global Variational Geometry.
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Amsterdam, Atlantis Press., 2015
ISBN 10: 946239072X
ISBN 13: 9789462390720
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 372 pp. Englisch. Bestandsnummer des Verkäufers 9789462390720
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Introduction to Global Variational Geometry
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Buch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Bestandsnummer des Verkäufers 9789462390720
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