SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM

Abhitosh Upadhyay; Ram Shankar Gupta; A. Sharfuddın

Research Article

SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM

Year 2012, Volume: 5 Issue: 1, 140 - 150, 30.04.2012

Abhitosh Upadhyay Ram Shankar Gupta A. Sharfuddın

Abstract

Keywords

Degenerate metric, lightlike hypersurfaces, indefinite generalized Sasakian space form

References

[1] Abdalla, B. E., Dillen, F.: A Ricci semi-symmetric hypersurface of Euclidean space which is not semi-symmetric. Proc. Amer. Math. Soc. 130, 6, 1805-1808, (2002).
[2] Alegre P., D. E. Blair and A. Carriazo: Generalized Sasakian space forms, Israel Journal of Mathematics 141(2004), 157-183.
[3] Bejancu, A.: Null hypersurfaces of semi-Euclidean spaces, Saitama Math J. 14, 25-40, (1996).
[4] Defever, F.: Ricci-semisymmetric hypersurfaces, Balkan J. of Geometry and its appl. 5, 1, 81-91, (2000).
[5] Deprez, J.: Semi-parallel surfaces in Euclidean space, J. of Geometry, 25, 192-200, (1985).
[6] Duggal, Krishan L. and Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
[7] Ludden, G. D.: Submanifolds of cosympletic manifolds, Journal of Differential Geometry 4 (1970), 237-244.
[8] Kupeli, D.N.: Singular Semi-Riemannian Geometry, Kluwer Acad. Publishers, Dordrecht, 1996.
[9] Matsuyama, Y.: Complete hypersurfaces with R.S = 0 in En+1, Proc. Amer. Math. Soc. 88, 119-123, (1983).
[10] Nomizu, K.: On hypersurfaces satisfying a certain condition on the curvature tensor, Tohoku Math. J. 20, 46-59, (1986).
[11] Ryan, P. J.: A class of complex hypersurfaces , Colloquium Math. 26, 175-182, (1972).
[12] Sahin, B.: Lightlike hypersurfaces of semi-Euclidean spaces satisfying curvature conditions of semi-symmetry type, Turk. J. Math. 31, 139-162, (2007).
[13] Szabo, Z.: Structure theorems on Riemannian spaces satisfying R(X, Y ).R = 0, the local version, J. Differential Geometry, 17, 531-582, (1982).
[14] Tanno, S.: Hypersurfaces satisfying a certain condition on the Ricci tensor, Tohoku Math. J. 21, 297-303, (1969).

Year 2012, Volume: 5 Issue: 1, 140 - 150, 30.04.2012

Abhitosh Upadhyay Ram Shankar Gupta A. Sharfuddın

Abstract

References

[1] Abdalla, B. E., Dillen, F.: A Ricci semi-symmetric hypersurface of Euclidean space which is not semi-symmetric. Proc. Amer. Math. Soc. 130, 6, 1805-1808, (2002).
[2] Alegre P., D. E. Blair and A. Carriazo: Generalized Sasakian space forms, Israel Journal of Mathematics 141(2004), 157-183.
[3] Bejancu, A.: Null hypersurfaces of semi-Euclidean spaces, Saitama Math J. 14, 25-40, (1996).
[4] Defever, F.: Ricci-semisymmetric hypersurfaces, Balkan J. of Geometry and its appl. 5, 1, 81-91, (2000).
[5] Deprez, J.: Semi-parallel surfaces in Euclidean space, J. of Geometry, 25, 192-200, (1985).
[6] Duggal, Krishan L. and Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
[7] Ludden, G. D.: Submanifolds of cosympletic manifolds, Journal of Differential Geometry 4 (1970), 237-244.
[8] Kupeli, D.N.: Singular Semi-Riemannian Geometry, Kluwer Acad. Publishers, Dordrecht, 1996.
[9] Matsuyama, Y.: Complete hypersurfaces with R.S = 0 in En+1, Proc. Amer. Math. Soc. 88, 119-123, (1983).
[10] Nomizu, K.: On hypersurfaces satisfying a certain condition on the curvature tensor, Tohoku Math. J. 20, 46-59, (1986).
[11] Ryan, P. J.: A class of complex hypersurfaces , Colloquium Math. 26, 175-182, (1972).
[12] Sahin, B.: Lightlike hypersurfaces of semi-Euclidean spaces satisfying curvature conditions of semi-symmetry type, Turk. J. Math. 31, 139-162, (2007).
[13] Szabo, Z.: Structure theorems on Riemannian spaces satisfying R(X, Y ).R = 0, the local version, J. Differential Geometry, 17, 531-582, (1982).
[14] Tanno, S.: Hypersurfaces satisfying a certain condition on the Ricci tensor, Tohoku Math. J. 21, 297-303, (1969).

There are 14 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Article
Authors	Abhitosh Upadhyay This is me Ram Shankar Gupta This is me A. Sharfuddın This is me
Publication Date	April 30, 2012
Published in Issue	Year 2012 Volume: 5 Issue: 1

Cite

APA	Upadhyay, A., Gupta, R. S., & Sharfuddın, A. (2012). SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM. International Electronic Journal of Geometry, 5(1), 140-150.
AMA	Upadhyay A, Gupta RS, Sharfuddın A. SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM. Int. Electron. J. Geom. April 2012;5(1):140-150.
Chicago	Upadhyay, Abhitosh, Ram Shankar Gupta, and A. Sharfuddın. “SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM”. International Electronic Journal of Geometry 5, no. 1 (April 2012): 140-50.
EndNote	Upadhyay A, Gupta RS, Sharfuddın A (April 1, 2012) SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM. International Electronic Journal of Geometry 5 1 140–150.
IEEE	A. Upadhyay, R. S. Gupta, and A. Sharfuddın, “SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM”, Int. Electron. J. Geom., vol. 5, no. 1, pp. 140–150, 2012.
ISNAD	Upadhyay, Abhitosh et al. “SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM”. International Electronic Journal of Geometry 5/1 (April 2012), 140-150.
JAMA	Upadhyay A, Gupta RS, Sharfuddın A. SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM. Int. Electron. J. Geom. 2012;5:140–150.
MLA	Upadhyay, Abhitosh et al. “SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM”. International Electronic Journal of Geometry, vol. 5, no. 1, 2012, pp. 140-5.
Vancouver	Upadhyay A, Gupta RS, Sharfuddın A. SEMI-SYMMETRIC AND RICCI SEMI-SYMMETRIC LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM. Int. Electron. J. Geom. 2012;5(1):140-5.