19 Sep 2011; IMS (UiTø), room U7=A152. Monday 14:00-15:00.

Konrad Schöbel (Friedrich-Schiller-Universität Jena, Germany)

The geometry of Killing tensors on the 3-sphere

Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton-Jacobi equation can be solved by a separation of variables. We establish purely algebraic equations characterizing the integrability of Killing tensors on constant curvature manifolds and solve them explicitly on the 3-sphere. We describe the projective variety of integrable Killing tensors and use this to classify all orthogonal separable coordinate systems. Several generalizations of this result will be proposed.