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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