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Introduction to Global Variational Geometry

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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 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 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 - 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

Pages: 354

Format: Hardcover

Publisher: Atlantis Press

Release: March 14, 2015

ISBN: 946239072X

ISBN 13: 9789462390720

Introduction to Global Variational Geometry

0/5 ( ratings)

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 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 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 - 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

Pages: 354

Format: Hardcover

Publisher: Atlantis Press

Release: March 14, 2015

ISBN: 946239072X

ISBN 13: 9789462390720

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