Calin / Chang Geometric Mechanics on Riemannian Manifolds

Applications to Partial Differential Equations
1. Auflage 2006
ISBN: 978-0-8176-4421-5
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 284 Seiten, Web PDF

Reihe: Mathematics and Statistics

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations.

Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. The text is enriched with good examples and exercises at the end of every chapter. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas.

Zielgruppe

Graduate

Autoren/Hrsg.

Calin, Ovidiu

Chang, Der-Chen

Inhaltsverzeichnis

Introductory Chapter.- Laplace Operators on Riemannian Manifolds.- Lagrangian Formalism on Riemannian Manifolds.- Harmonic Maps from a Lagrangian Viewpoint.- Conservation Theorems.- Hamiltonian Formalism.- Hamilton-Jacobi Theory.- Minimal Hypersurfaces.- Radially Symmetric Spaces.- Fundamental Solutions for Heat Operators with Potentials.- Fundamental Solutions for Elliptic Operators.- Mechanical Curves.