2006/10/06 by Luca Degiovanni, Giovanni Rastelli
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Nonlinear Waves and Solitons #Tensor decomposition and applications #nlin.SI
paper · pdf · doi:10.1063/1.2747611
26 pages, 5 low resolution pictures
arxiv created 2006/10/06 · openalex publication_date 2007/07/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper the geometric theory of separation of variables for the 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 complexifying the manifold but just by considering complex-valued functions on it. The simple formalism introduced in the paper allows us to extend in a very natural way the classical results on separation of variables (including Levi-Civita criterion and Stäckel-Eisenhart theory) to the complex case. Only orthogonal variables are considered.