V.V. Slavskii
On a theorem of Fermi

Comment.Math.Univ.Carolinae 37,4 (1996) 867-872.

Abstract:Conformally flat metric $\bar g$ is said to be Ricci superosculating with $g$ at the point $x_0$ if $g_{ij}(x_0)=\bar g_{ij}(x_0)$, $\Gamma _{ij}^k(x_0)=\bar \Gamma _{ij}^k(x_0)$, $R_{ij}^k(x_0)=\bar R_{ij}^k(x_0)$, where $R_{ij}$ is the Ricci tensor. In this paper the following theorem is proved: \vskip \medskipamount \par {If $ \gamma $ is a smooth curve of the Riemannian manifold $M$ {(}without self-crossing{)}, then there is a neighbourhood of $ \gamma $ and a conformally flat metric $\bar g$ which is the Ricci superosculating with $g$ along the curve $\gamma $.}

Keywords: conformal connection, development
AMS Subject Classification: 53A30, 53C20

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