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Complex variables for separation of Hamilton-Jacobi equation on real pseudo-Riemannian manifolds | | Luca Degiovanni
; Giovanni Rastelli
; | | Date: |
6 Oct 2006 | | Subject: | Exactly Solvable and Integrable Systems | | Abstract: | In this paper the geometric theory of separation of variables for time-independent Hamilton-Jacobi equation is extended to include the case of complex eigenvalues of a Killing tensor on pseudo-Riemannian manifolds. This task is performed without to complexify the manifold but just considering complex-valued functions on it. The simple formalism introduced allows to extend in a very natural way the classical results on separation of variables (including Levi-Civita criterion and Stackel-Eisenhart theory) to the complex case. Orthogonal variables only are considered. | | Source: | arXiv, nlin/0610012 | | Services: | Forum | Review | PDF | Favorites | |
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