Totally Contact Umbilical Radical Transversal Lightlike Submanifolds Of An Almost Contact Manifold With B-Metric
DOI:
https://doi.org/10.24297/jam.v13i4.6234Keywords:
Almost contact manifolds, B-metric, Totally umbilical, transversal lightlike submanifolds.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.
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References
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[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).
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Published
2017-07-03
How to Cite
Devgan, A., & Nagaich, R. K. (2017). Totally Contact Umbilical Radical Transversal Lightlike Submanifolds Of An Almost Contact Manifold With B-Metric. JOURNAL OF ADVANCES IN MATHEMATICS, 13(4), 7286–7294. https://doi.org/10.24297/jam.v13i4.6234
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