EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZ SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

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

Abstract
We study Einstein lightlike hypersurfaces M of a Lorentzian space form $\small{\tilde{M}(c)}$ admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field $\small{{\zeta}}$ of $\small{\tilde{M}}$ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.
Keywords
screen conformal;lightlike hypersurface;Einstein manifold;semisymmetric non-metric connection;
Language
English
Cited by
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LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION, East Asian mathematical journal, 2015, 31, 1, 33
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NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE KAEHLER MANIFOLDS ADMITTING NON-METRIC π-CONNECTIONS, Communications of the Korean Mathematical Society, 2014, 29, 4, 539
3.
TWO CHARACTERIZATION THEOREMS FOR LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM, Honam Mathematical Journal, 2013, 35, 3, 329
4.
NON-TANGENTIAL HALF LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS WITH SEMI-SYMMETRIC NON-METRIC CONNECTIONS, Journal of the Korean Mathematical Society, 2014, 51, 2, 311
5.
SINGULAR THEOREMS FOR LIGHTLIKE SUBMANIFOLDS IN A SEMI-RIEMANNIAN SPACE FORM, East Asian mathematical journal, 2014, 30, 3, 371
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HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION, The Pure and Applied Mathematics, 2014, 21, 1, 39
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LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD WITH A NON-METRIC θ-CONNECTION, The Pure and Applied Mathematics, 2014, 21, 4, 229
8.
NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE TRANS-SASAKIAN MANIFOLDS WITH NON-METRIC 𝜃-CONNECTIONS, Communications of the Korean Mathematical Society, 2015, 30, 1, 35
References
1.
N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection on a Rie-mannian manifold, Indian J. Pure Appl. Math. 23 (1992), no. 6, 399-409.

2.
G. de Rham, Sur la reductibilite dun espace de Riemannian, Comm. 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 D. H. Jin, A Classification of Einstein lightlike hypersurfaces of a Lorentzian space form, J. Geom. Phys. 60 (2010), no. 12, 1881-1889.

6.
K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.

7.
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, Cambridge, 1973.

8.
D. H. Jin, Lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math. 19 (2012), no. 3, 211-228.

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

10.
D. N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Acad. Publishers, Dordrecht, 1996.

11.
B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.

12.
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.