ASCREEN LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Title & Authors
ASCREEN LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION
Jin, Dae Ho;

Abstract
We study lightlike hypersurfaces of a semi-Riemannian space form $\small{\tilde{M}(c)}$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\small{\tilde{M}(c)}$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.
Keywords
totally geodesic;ascreen lightlike hypersurface;semi-symmetric non-metric connection;
Language
English
Cited by
1.
NON-TANGENTIAL HALF LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS WITH SEMI-SYMMETRIC NON-METRIC CONNECTIONS,;

대한수학회지, 2014. vol.51. 2, pp.311-323
References
1.
N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), no. 6, 399-409.

2.
G. de Rham, Sur la reductibilite d'un espace de Riemannian, Comment. Math. Helv. 26 (1952), 328-344.

3.
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.

4.
K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.

5.
K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.

6.
D. H. Jin, Transversal half lightlike submanifolds of an indefinite Sasakian manifold, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 18 (2011), no. 1, 51-61.

7.
D. H. Jin, Special half lightlike submanifolds of an indefinite cosymplectic manifold, J. Funct. Spaces Appl. 2012 (2012), Art. ID 636242, 16 pp.

8.
D. H. Jin, Ascreen lightlike hypersurfaces of an indefinite Sasakian manifold, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 20 (2013), no. 1, 25-35.

9.
D. H. Jin, Geometry of lightlike hypersurfaces of a semi-Riemannian space form with a semi-symmetric non-metric connection, submittied in Indian J. Pure Appl. Math.

10.
D. H. Jin, Einstein lightlike hypersurfaces of a Lorentz space form with a semi-symmetric non-metric connection, accepted in Bull. Korean Math. Soc.

11.
D. H. Jin, Two characterization theorems for lightlike geometry, submitted in Honam Math. J.

12.
D. H. Jin, A classification of screen quasi-conformal Einstein lightlike hypersurfaces of a semi-Riemannian space form with a semi-symmetric non-metric connection, submitted in J. Fun. Sp. Math.

13.
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.