Atlantis Studies in Variational Geometry

Introduction to Global Variational Geometry

Authors: Krupka, Demeter

  • Systematic exposition of the higher-order global variational theory on fibered spaces with complete proofs of basic results
  • First systematic treatment of variational calculus and its applications for manifoldsĀ 
  • Covers applications of variational theory in modern theoretical physics
  • Prepares the reader for research in the local and global inverse problem of the calculus of variations for partial differential equations
  • Variational sequence theory and its consequences are explained, based on elementary sheaf theory
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eBook $79.99
price for USA (gross)
  • ISBN 978-94-6239-073-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-94-6239-072-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (8 chapters)

  • Jet Prolongations of Fibered Manifolds

    Krupka, Demeter

    Pages 1-33

  • Differential Forms on Jet Prolongations of Fibered Manifolds

    Krupka, Demeter

    Pages 35-84

  • Formal Divergence Equations

    Krupka, Demeter

    Pages 85-101

  • Variational Structures

    Krupka, Demeter

    Pages 103-168

  • Invariant Variational Structures

    Krupka, Demeter

    Pages 169-185

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-94-6239-073-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-94-6239-072-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Global Variational Geometry
Authors
Series Title
Atlantis Studies in Variational Geometry
Series Volume
1
Copyright
2015
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author
eBook ISBN
978-94-6239-073-7
DOI
10.2991/978-94-6239-073-7
Hardcover ISBN
978-94-6239-072-0
Series ISSN
2214-0700
Edition Number
1
Number of Pages
XVII, 354
Topics