Conformal Killing tensors with vanishing torsion and the separation of variables in the hamilton-Jacobi equation

摘要

If a Riemannian manifold admits a conformal Killing tensor whose torsion, in the sense of Nijenhuis, vanishes, and whose eigenfunctions are independent, then the hamilton-Jacobi equation for its geodescis is solvable by separation of variables. The paper is devoted to developing a theory of this class of conformal Killing tensors, including an explanation of this result.