In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold and a symmetric 2-tensor , construct a metric on whose Ricci tensor equals . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative...
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