School Seminars and Colloquia

Some geometrical aspects of Hamilton-Jacobi separability

AMSI Seminar

by Willy Sarlet


Institution: Department of Mathematical Physics and Astronomy Ghent University, Belgium
Date: Thu 16th June 2005
Time: 2:00 PM
Location: AMSI seminar room, 111 Barry Street

Abstract: After a brief review of classical Lagrange and Hamilton equations, we recall the ideas behind setting up the partial differential equation, known as the hamilton-Jacobi equation, and explain Stäckel's theorem about separability of this equation in orthogonal coordinates. We then proceed to describe 'special conformal Killing tensors; on a pseudo-Riemannian manifold: they were discovered first by Benenti, and provide an interesting geometrical characterization of a subclass of Stäckel systems. Such tensors are further closely related to the existence of a so-called Poisson-Nijenhuis structure on the cotangent bundle T*Q of the configuration manifold. My own involvement in the theory, recently, has been to understand how much geometical structures can also be conceived in a natural way on a tangent bundle and that's where most of the second half of the talk will be about.

For More Information: Geoff Prince tel. 8344-1775 email: geoff.prince@amsi.org.au