Semi-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 2,  2016, pp.625-638
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.2.625
Title & Authors
Semi-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

Abstract
In this paper, we introduce the notion of semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions $\small{D_1}$, $\small{D_2}$ and RadTM on semi-slant lightlike submanifolds of an indefinite Sasakian manifold have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.
Keywords
Semi-Riemannian manifold;degenerate metric;radical distribution;screen distribution;screen transversal vector bundle;lightlike transversal vector bundle;Gauss and Weingarten formulae;
Language
English
Cited by
References
1.
C. L. Bejan and K. L. Duggal, Global Lightlike Manifolds and Harmonicity, Kodai Math. J., 28(2005), 131-145.

2.
D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2002.

3.
J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Slant Submanifolds in Sasakian manifolds, Glasgow Math J., 42(2000), 125-138.

4.
J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Semi-slant Submanifolds of a Sasakian manifold, Geometriae Dedicata, 78(1999), 183-199.

5.
B. Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit, Leuven, 1990.

6.
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Vol. 364 of Mathematics and its applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.

7.
K. L. Duggal and B. Sahin, Differential Geomety of Lightlike Submanifolds, Birkhauser Verlag AG, Basel, Boston, Berlin, 2010.

8.
K. L. Duggal and B. Sahin, Lightlike Submanifolds of Indefinite Sasakian Manifolds, Int. J. of Math. Math. Sci., Article ID 57585, 2007.

9.
D. L. Johnson and L. B. Whitt, Totally Geodesic Foliations, J. Differential Geometry, 15(1980), 225-235.

10.
A. Lotta, Slant Submanifolds in Contact geometry, Bull. Math. Soc. Roumanie, 39(1996), 183-198.

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

12.
B. Sahin, Screen Slant Lightlike Submanifolds, Int. Electronic J. of Geometry, 2(2009), 41-54.

13.
B. Sahin and C. Yildirim, Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds, Faculty of Sci. and Math., Univ. of Nis, Serbia, 2(2012), 277-287.

14.
S. S. Shukla and A. Yadav, Lightlike submanifolds of indefinite para-Sasakian manifolds, Matematicki Vesnik, 66(4)(2014), 371-386.

15.
S. S. Shukla and A. Yadav, Radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, Demonstratio Math., 47(4)(2014), 994-1011.