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http://dx.doi.org/10.5666/KMJ.2017.57.3.503

Totally Umbilical Slant Lightlike Submanifolds of Indefinite Kaehler Manifolds  

Sachdeva, Rashmi (Department of Basic and Applied Sciences, Punjabi University)
Kumar, Rakesh (Department of Basic and Applied Sciences, Punjabi University)
Bhatia, Satvinder Singh (School of Mathematics, Thapar University)
Publication Information
Kyungpook Mathematical Journal / v.57, no.3, 2017 , pp. 503-516 More about this Journal
Abstract
In this paper, we study totally umbilical slant lightlike submanifolds of indefinite Kaehler manifolds. We prove that there do not exist totally umbilical proper slant lightlike submanifolds in indefinite Kaehler manifolds other than totally geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally umbilical proper slant lightlike submanifolds of indefinite Kaehler space forms. Finally, we give a characterization theorem on minimal slant lightlike submanifolds.
Keywords
Slant lightlike submanifolds; totally umbilical lightlike submanifolds; totally geodesic lightlike submanifolds;
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1 M. Barros and A. Romero, Indefinite Kaehler manifolds, Math. Ann., 261(1982), 55-62.   DOI
2 C. L. Bejan and K. L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J., 28(2005), 131-145.   DOI
3 J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J., 42(2000), 125-138.   DOI
4 J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez, Semi-slant sub-manifolds of a Sasakian manifold, Geom. Dedicata., 78(1999), 183-199.   DOI
5 B. Y. Chen, Slant immersions, Bull. Austral. Math. Soc., 41(1990), 135-147.   DOI
6 B. Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit, Leuven, (1990).
7 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).
8 K. L. Duggal and D. H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J., 26(2003), 49-68.   DOI
9 K. L. Duggal and B. Sahin, Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 106(2005), 125-153.
10 E. J. Flaherty, Hermitian and Kaehlerian Geometry in Relativity, Lecture Notes in Physics, 46, Springer-Verlag, (1976).
11 R. S. Gupta, A. Upadhyay and A. Sharfuddin, Slant lightlike submanifolds of indefinite Cosymplectic manifolds, Mediterr. J. Math., 8(2011), 215-227.   DOI
12 A. Lotta, Slant submanifolds in contact geometry, Bull. Soc. Sci. Math. Roumanie, 39(1996), 183-198.
13 A. Lotta, Three dimensional slant submanifolds of K-contact manifolds, Balkan J. Geom. Appl., 3(1998), 37-51.
14 B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, (1983).
15 N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi Secct. I a Mat., 40(1994), 55-61.
16 Rashmi Sachdeva, Rakesh Kumar and S. S. Bhatia, Nonexistence of totally contact umbilical slant lightlike submanifolds of indefinite Cosymplectic manifolds, ISRN Geometry, Volume 2013, Article ID 231869, 8 pages.
17 Rashmi Sachdeva, Rakesh Kumar and S. S. Bhatia, Non existence of totally contact umbilical proper slant lightlike submanifold of indefinite Sasakian manifolds, Bull. Iranian Math. Soc., 40(5)(2014), 1135-1151.
18 Rashmi Sachdeva, Rakesh Kumar and S. S. Bhatia, Warped product slant lightlike submanifolds of indefinite Sasakian manifolds, Balkan J. Geom. Appl., 20(1)(2015), 98-108.
19 Rashmi Sachdeva, Rakesh Kumar and S. S. Bhatia, Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds, Tamkang J. Maths., 46(2)(2015), 179-191.   DOI
20 Rashmi Sachdeva, Rakesh Kumar and S. S. Bhatia, Totally umbilical hemi-slant light-like submanifolds, New York J. Math., 21(2015), 191-203.
21 B. Sahin, Every totally umbilical proper slant submanifolds of a Kaehler manifold is totally geodesic, Result. Math., 54(2009), 167-172.   DOI
22 B. Sahin, Slant lightlike submanifolds of indefinite Hermitian manifolds, Balkan J. Geom. Appl., 13(2008), 107-119.