Totally Contact Umbilical Radical Transversal Lightlike Submanifolds Of An Almost Contact Manifold With B-Metric

Main Article Content

Anu Devgan R. K. Nagaich

Abstract

In the present paper, we study the geometry of totally contact umbilical radical transversal lightlike submanifolds and totally contact umbilical CR- submanifold of an indenite Sasaki-like almost contact manifold with B-metric. We nd the necessary and sucient condition for the characterization of the induced connection to be a metric connection. Finally, we have proved that for a totally contact umbilical CR-submanifold, totally contact umbilical radical transversal lightlike submanifold is a totally geodesic radical transversal lightlike submanifold.

Article Details

How to Cite
DEVGAN, Anu; NAGAICH, R. K.. Totally Contact Umbilical Radical Transversal Lightlike Submanifolds Of An Almost Contact Manifold With B-Metric. JOURNAL OF ADVANCES IN MATHEMATICS, [S.l.], v. 13, n. 4, p. 7286-7294, aug. 2017. ISSN 2347-1921. Available at: <https://cirworld.com/index.php/jam/article/view/6234>. Date accessed: 20 oct. 2017. doi: https://doi.org/10.24297/jam.v13i4.6234.
Section
Articles

References

[1] Bejancu A., CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc., 69 (1978), 135{142.
[2] Bejancu A., CR-submanifolds of a Kaehler manifold-II, Trans. Amer. Math. Soc., 250 (1979), 333{345.
[3] Duggal K. L., Bejancu A. , Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, 364 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, (1996).
[4] Duggal K. L. and Jin D. H., Totally umbilical lightlike submanifolds, Kodai Math. J., 26 (2003), 49{68.
[5] Duggal K. L. and Sahin B., Lightlike submanifolds of indenite Sasakian manifolds, Int. Jour. Math and Math. Sci., 26 (2007), 49{68.
[6] Ganchev, G., Mihova,V., Gribachev, K., Almost contact manifolds with B-metric, Math. Balkanica (N.S.), 7(3{4) (1993), 261{276.
[7] Matsumoto K., On contact CR-submanifolds of Sasakian manifolds, International J. Math. Math. Sci., 6(2)(1983), 313{326.
[8] Ivanov S., Manev H. and Manev M., Sasaki-like Almost contact complex Riemannian manifolds, J. Geom and Physics, 107 (2016), 136-148.
[9] Nakova G., Some lightlike submanifolds of almost complex manifolds with Norden met- ric, J. Geometry, 103 (2012), 293{312.
[10] Yildirim C. and Sahin B., Transversal lightlike submanifolds of indenite Sasakian manifolds, Turk J Math., 34 (2010), 561{583.
[11] Yano K. and Kon M., Dierential geometry of CR submanifolds, Geometria Dedicata, 10(1981), 369{391.
[12] Yano K. and Kon M., CR submanifolds of Kaehlerian and Sasakian manifolds, World Scientic, (1984).