Introduction to Global Variational Geometry

• Main Author: Krupka, Demeter (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
• Series: Atlantis Studies in Variational Geometry, 1
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential geometry.; Calculus of variations.; Physics.; Gravitation.; Global Analysis and Analysis on Manifolds.; Differential Geometry.; Calculus of Variations and Optimal Control; Optimization.; Theoretical, Mathematical and Computational Physics.; Classical and Quantum Gravitation, Relativity Theory.

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...

Table of Contents:

• 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.