| Title:
|
On a theorem of Fermi (English) |
| Author:
|
Slavskii, V. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
867-872 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $.\/} (English) |
| Keyword:
|
conformal connection |
| Keyword:
|
development |
| MSC:
|
53A30 |
| MSC:
|
53B20 |
| MSC:
|
53C20 |
| idZBL:
|
Zbl 0888.53030 |
| idMR:
|
MR1440717 |
| . |
| Date available:
|
2009-01-08T18:28:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118894 |
| . |
| Reference:
|
[1] Cartan E.: Leçons sur la Géometrie des Espaces de Riemann.Gauthier-Villars, Paris (1928), 242. MR 0020842 |
| Reference:
|
[2] Cartan E.: Les espaces à connection conforme.Ann. Soc. Po. Math. (1923), 2 171-221. |
| Reference:
|
[3] Slavskii V.V.: Conformal development of the curve on the Riemannian manifold in the Minkowski space.Siberian Math. Journal 37 3 (1996), 676-699. MR 1434711 |
| Reference:
|
[4] Akivis M.A., Konnov V.V.: Sense local aspects of the theory of conformal structure.Russian Math. Surveys (1993), 48 3-40. MR 1227946 |
| Reference:
|
[5] Slavskii V.V.: Conformally flat metrics and the geometry of the pseudo-Euclidean space.Siberian Math. Jour. (1994), 35 3 674-682. MR 1292228 |
| Reference:
|
[6] Besse A.L.: Einstein Manifolds.Erg. Math. Grenzgeb. 10, Berlin-Heidelberg-New York (1987). Zbl 0613.53001, MR 0867684 |
| Reference:
|
[7] Reshetnyak Yu.G.: On the lifting of the non-regular path in the bundle manifold and its applications.Siberian Math. Jour. (1975), 16 3 588-598. |
| Reference:
|
[8] Gray A., Vonhecke L.: The volumes of tubes about curves in a Riemannian manifold.Proc. London Math. Soc. (1982), 44 2 215-243. MR 0647431 |
| . |
