| Title:
|
Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection (English) |
| Author:
|
Yücesan, Ahmet |
| Author:
|
Ayyildiz, Nihat |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
77-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection. Eventually, we establish conformal equations of Gauss curvature and Codazzi-Mainardi. (English) |
| Keyword:
|
semi-symmetric metric connection |
| Keyword:
|
Levi-Civita connection |
| Keyword:
|
mean curvature |
| Keyword:
|
Ricci tensor |
| Keyword:
|
conformally flat |
| MSC:
|
53B15 |
| MSC:
|
53B30 |
| MSC:
|
53C05 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 1212.53023 |
| idMR:
|
MR2431233 |
| . |
| Date available:
|
2008-06-06T22:52:53Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108098 |
| . |
| Reference:
|
[1] Agricola, I., Friedrich, Th.: On the holonomy of connections with skew-symmetric torsion.Math. Ann. 328 (4) (2004), 711–748. Zbl 1055.53031, MR 2047649, 10.1007/s00208-003-0507-9 |
| Reference:
|
[2] Cartan, E.: Sur les variétés à connexion affine et la théorie de la relativité généralisée $($deuxiéme partie$)$.Ann. Ecole Norm. Sup. 42 (1925), 17–88. MR 1509263 |
| Reference:
|
[3] Duggal, K., Sharma, R.: Semi-symmetric metric connections in a semi-Riemannian manifold.Indian J. Pure Appl. Math. 17 (11) (1986), 1276–1282. Zbl 0607.53012, MR 0868964 |
| Reference:
|
[4] Friedmann, A., Schouten, J. A.: Über die Geometrie der halbsymmetrischen Übertragungen.Math. Z. 21 (1924), 211–223. MR 1544701, 10.1007/BF01187468 |
| Reference:
|
[5] Hayden, H. A.: Subspace of a space with torsion.Proc. London Math. Soc. 34 (1932), 27–50. |
| Reference:
|
[6] Imai, T.: Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection.Tensor (N.S.) 23 (1972), 300–306. Zbl 0262.53041, MR 0336597 |
| Reference:
|
[7] Imai, T.: Notes on semi-symmetric metric connections.Tensor (N.S.) 24 (1972), 293–296. Zbl 0251.53038, MR 0375121 |
| Reference:
|
[8] Konar, A., Biswas, B.: Lorentzian manifold that admits a type of semi-symmetric metric connection.Bull. Calcutta Math. Soc. 93 (5) (2001), 427–437. Zbl 1021.53043, MR 1909170 |
| Reference:
|
[9] O’Neill, B.: Semi-Riemannian geometry with applications to relativity.Academic Press, London, 1983. MR 0719023 |
| Reference:
|
[10] Yano, K.: On semi-symmetric metric connection.Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. Zbl 0213.48401, MR 0275321 |
| . |
