Demeter Krupka's Introduction to Global Variational Geometry (Atlantis PDF

By Demeter Krupka

ISBN-10: 946239072X

ISBN-13: 9789462390720

The ebook is dedicated to contemporary learn within the worldwide variational concept on soft manifolds. Its major goal is an extension of the classical variational calculus on Euclidean areas to (topologically nontrivial) finite-dimensional delicate manifolds; to this objective the equipment of world research of differential kinds are used. Emphasis is put on the rules of the idea of variational functionals on fibered manifolds - correct geometric buildings for variational ideas in geometry, actual box conception and higher-order fibered mechanics. The publication chapters contain: - foundations of jet bundles and research of differential varieties and vector fields on jet bundles, - the speculation of higher-order necessary variational functionals for sections of a fibred house, the (global) first variational formulation in infinitesimal and fundamental kinds- extremal stipulations and the dialogue of Noether symmetries and generalizations,- the inverse difficulties of the calculus of diversifications of Helmholtz variety- variational series thought and its results for the worldwide inverse challenge (cohomology conditions)- examples of variational functionals of mathematical physics. entire formulations and proofs of all simple assertions are given, in accordance with theorems of worldwide research defined within the Appendix.

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Introduction to Global Variational Geometry (Atlantis Studies in Variational Geometry) by Demeter Krupka

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