Some geometrical aspects of Hamilton-Jacobi separability
by Willy Sarlet
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 StÃ¤ckel'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 StÃ¤ckel 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.
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