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Conformally flat metric $\overline{g}$ is said to be Ricci superosculating with $g$ at the point $x_0$ if $g_{ij}\left(x_0\right)={\overline{g}}_{ij}\left(x_0\right)$, ${\Gamma }_{ij}^k\left(x_0\right)={\overline{\Gamma }}_{ij}^k\left(x_0\right)$, $R_{ij}^k\left(x_0\right)={\overline{R}}_{ij}^k\left(x_0\right)$, where $R_{ij}$ is the Ricci tensor. In this paper the following theorem is proved: ((

In this paper we investigate one-dimensional sectional curvatures of Riemannian manifolds, conformal deformations of the Riemannian metrics and the structure of locally conformally homogeneous Riemannian manifolds. We prove that the nonnegativity of the one-dimensional sectional curvature of a homogeneous Riemannian space attracts nonnegativity of the Ricci curvature and we show that the inverse is incorrect with the help of the theorems O. Kowalski-S. Nikčevi'c [K-N], D. Alekseevsky-B. Kimelfeld...