Complex variables for separation of Hamilton-Jacobi equation on real pseudo-Riemannian manifolds

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.

26 pages, 5 low resolution pictures

References in corpus (2)

• Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
• Complex variables for separation of Hamilton-Jacobi equation on three-dimensional Minkowski space

Cited by in corpus (2)

• Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space
• Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds