The Convenient Setting of Global Analysis
by Andreas Kriegl, Peter W. Michor
Publisher: American Mathematical Society 1997
ISBN/ASIN: 0821807803
ISBN-13: 9780821807804
Number of pages: 624
Description:
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. Many applications are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
Download or read it online for free here:
Download link
(4MB, PDF)
Similar books
Exterior Differential Systems and Euler-Lagrange Partial Differential Equationsby R. Bryant, P. Griffiths, D. Grossman - University Of Chicago Press
The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.
(19211 views)
Lectures on Fibre Bundles and Differential Geometryby J.L. Koszul - Tata Institute of Fundamental Research
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).
(12473 views)
Synthetic Differential Geometryby Anders Kock - Cambridge University Press
Synthetic differential geometry is a method of reasoning in differential geometry and calculus. This book is the second edition of Anders Kock's classical text, many notes have been included commenting on new developments.
(15624 views)
Lectures on Exterior Differential Systemsby M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
(14089 views)