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http://dx.doi.org/10.4134/BKMS.2010.47.5.1089

LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION  

Yucesan, Ahmet (SULEYMAN DEMIREL UNIVERSITY DEPARTMENT OF MATHEMATICS)
Yasar, Erol (MERSIN UNIVERSITY DEPARTMENT OF MATHEMATICS)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.5, 2010 , pp. 1089-1103 More about this Journal
Abstract
In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.
Keywords
lightlike submanifolds; semi-symmetric non-metric connection; Levi-Civita connection; Ricci tensor;
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1 E. Yasar, A. C. Coken, and A. Yucesan, Lightlike hypersurfaces in semi-Riemannian manifold with semi-symmetric non-metric connection, Math. Scand. 102 (2008), no. 2, 253-264.   DOI
2 N. S. Ageshe and M. R. Chafle, A semi-symmetric nonmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), no. 6, 399-409.
3 N. S. Ageshe and M. R. Chafle, On submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection, Tensor (N.S.) 55 (1994), no. 2, 120-130.
4 A. Bejancu and K. L. Duggal, Lightlike submanifolds of semi-Riemannian manifolds, Acta Appl. Math. 38 (1995), no. 2, 197-215.   DOI
5 U. C. De and D. Kamilya, Hypersurfaces of a Riemannian manifold with semisymmetric non-metric connection, J. Indian Inst. Sci. 75 (1995), no. 6, 707-710.
6 K. L. Duggal and A. Bejancu, Lightlike Submanifold of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers Group, Dordrecht, 1996.
7 K. L. Duggal and R. Sharma, Semisymmetric metric connections in a semi-Riemannian manifold, Indian J. Pure Appl. Math. 17 (1986), no. 11, 1276-1283.
8 K. L. Duggal and D. H. Jin, Half lightlike submanifolds of codimension 2, Math. J. Toyama Univ. 22 (1999), 121-161.
9 H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.   DOI
10 E. Kilic, B. Sahin, H. B. Karadag, and R. Gunes, Coisotropic submanifolds of a semi-Riemannian manifold, Turkish J. Math. 28 (2004), no. 4, 335-352.
11 B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, London, 1983.
12 B. Prasad and R. K. Verma, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Bull. Calcutta Math. Soc. 96 (2004), no. 6, 483-488.
13 J. Sengupta, D. C. De, and T. Q. Binh, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 31 (2000), no. 12, 1659-1670.
14 K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.