Geometric Mechanics on Riemannian Manifolds

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.

A geometric approach to problems in physics, many of which cannot be solved by any other methods Text is enriched with good examples and exercises at the end of every chapter Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Contenu
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.