Geodesic
Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection
Archivum mathematicum, Tome 44 (2008) no. 1, pp. 77-88 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53B15, 53B30, 53C05, 53C50
Keywords: semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat 
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Yücesan, Ahmet; Ayyildiz, Nihat. Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection. Archivum mathematicum, Tome 44 (2008) no. 1, pp. 77-88. http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a8/

[1] Agricola, I., Friedrich, Th.: On the holonomy of connections with skew-symmetric torsion. Math. Ann. 328 (4) (2004), 711–748. | DOI | MR | Zbl

[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

[3] Duggal, K., Sharma, R.: Semi-symmetric metric connections in a semi-Riemannian manifold. Indian J. Pure Appl. Math. 17 (11) (1986), 1276–1282. | MR | Zbl

[4] Friedmann, A., Schouten, J. A.: Über die Geometrie der halbsymmetrischen Übertragungen. Math. Z. 21 (1924), 211–223. | DOI | MR

[5] Hayden, H. A.: Subspace of a space with torsion. Proc. London Math. Soc. 34 (1932), 27–50.

[6] Imai, T.: Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection. Tensor (N.S.) 23 (1972), 300–306. | MR | Zbl

[7] Imai, T.: Notes on semi-symmetric metric connections. Tensor (N.S.) 24 (1972), 293–296. | MR | Zbl

[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. | MR | Zbl

[9] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press, London, 1983. | MR

[10] Yano, K.: On semi-symmetric metric connection. Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. | MR | Zbl