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Currently displaying 1 – 2 of 2

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On a theorem of Fermi

Viktor V. Slavskii — 1996

Commentationes Mathematicae Universitatis Carolinae

Conformally flat metric $\bar{g}$ is said to be Ricci superosculating with $g$ at the point $x_{0}$ if $g_{i j} (x_{0}) = {\bar{g}}_{i j} (x_{0})$ , $Γ_{i j}^{k} (x_{0}) = {\bar{Γ}}_{i j}^{k} (x_{0})$ , $R_{i j}^{k} (x_{0}) = {\bar{R}}_{i j}^{k} (x_{0})$ , where $R_{i j}$ is the Ricci tensor. In this paper the following theorem is proved: ((

Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces

Eugene D. Rodionov; Viktor V. Slavskii — 2002

Commentationes Mathematicae Universitatis Carolinae

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...

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