On a theorem of Fermi
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 867-872
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: \medskip {\sl If $\,\gamma $ is a smooth curve of the Riemannian manifold $M$ {\rm (}without self-crossing{\rm (}, 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 $.\/}
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: \medskip {\sl If $\,\gamma $ is a smooth curve of the Riemannian manifold $M$ {\rm (}without self-crossing{\rm (}, 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 $.\/}
@article{CMUC_1996_37_4_a18,
author = {Slavskii, V. V.},
title = {On a theorem of {Fermi}},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {867--872},
year = {1996},
volume = {37},
number = {4},
mrnumber = {1440717},
zbl = {0888.53030},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_1996_37_4_a18/}
}
Slavskii, V. V. On a theorem of Fermi. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 867-872. http://geodesic.mathdoc.fr/item/CMUC_1996_37_4_a18/