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The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure

Sergey E. Stepanov; Irina I. Tsyganok; Marina B. Khripunova — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.

On Uniqueness Theoremsfor Ricci Tensor

Marina B. Khripunova; Sergey E. Stepanov; Irina I. Tsyganok; Josef Mikeš — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$ , construct a metric on $M$ whose Ricci tensor equals $r$ . 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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The Killing Tensors on an n -dimensional Manifold with S L ( n , ) -structure

On Uniqueness Theoremsfor Ricci Tensor

The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure