Structural equations for Killing tensors of arbitrary rank

An algorithm is given for bringing the equations of monomial first integrals of arbitrary degree of the geodesic motion in a Riemannian space Vn into the form (FA) k = ∑ B ΓkABFB . The FA are the components of a Killing tensor Ki1...ir of arbitrary rank r and its symmetrized covariant derivatives. Explicit formulas are given for rank 1,2 and 3. Killing tensor equations in structural form allow the formulation of algebraic integrability conditions and are supposed to be well suited for integration as it is demonstrated in the case of flat space. An alternative proof of the reducibility of these Killing tensors is given which shows the correspondence to structural equations for rank 2 Killing tensors as formulated by Hauser & Malhiot. They used tensors with different symmetry properties. PACS numbers: 0420, 0240, 0490, 0290 By-line: Structural Equations for Killing Tensors