# On a theorem of Fermi

Commentationes Mathematicae Universitatis Carolinae (1996)

- Volume: 37, Issue: 4, page 867-872
- ISSN: 0010-2628

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topSlavskii, Viktor V.. "On a theorem of Fermi." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 867-872. <http://eudml.org/doc/247877>.

@article{Slavskii1996,

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: 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 $.},

author = {Slavskii, Viktor V.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {conformal connection; development; conformal connection; development},

language = {eng},

number = {4},

pages = {867-872},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On a theorem of Fermi},

url = {http://eudml.org/doc/247877},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Slavskii, Viktor V.

TI - On a theorem of Fermi

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1996

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 37

IS - 4

SP - 867

EP - 872

AB - 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: 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 $.

LA - eng

KW - conformal connection; development; conformal connection; development

UR - http://eudml.org/doc/247877

ER -

## References

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- Slavskii V.V., Conformally flat metrics and the geometry of the pseudo-Euclidean space, Siberian Math. Jour. (1994), 35 3 674-682. (1994) MR1292228
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