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Catalogue Information
Field name	Details
Dewey Class	514.74
Title	Introduction to Global Variational Geometry ([EBook]) / by Demeter Krupka.
Author	Krupka, Demeter
Other name(s)	SpringerLink (Online service)
Publication	Paris : : Atlantis Press : : Imprint: Atlantis Press, , 2015.
Physical Details	XVII, 354 p. : online resource.
Series	Atlantis Studies in Variational Geometry 2214-0700 ; ; 1
ISBN	9789462390737
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.2991/978-94-6239-073-7
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Classical and Quantum Gravitation, Relativity Theory . Differential Geometry . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Gravitation . Manifolds (Mathematics) . Mathematics . Physics . Theoretical, Mathematical and Computational Physics . Authors: Krupka, Demeter . Corporate Authors: SpringerLink (Online service) . Series: Atlantis Studies in Variational Geometry . Classification: 514.74 .

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Introduction to Global Variational Geometry

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