Structural equations for killing tensors of arbitrary rank Original Research Article

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 = ΣBΛkABFB. The FA are the components of a Killing tensor Ki|…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. A method based on integrability conditions being algebraic is given to compute in a single generic point of pace-time numerically the number of nontrivial Killing tensors using numerical values for the Riemann tensor and its derivatives.