Screen Transversal Lightlike Submanifolds of Indefinite Kenmotsu Manifolds
DOI:
https://doi.org/10.5644/SJM.07.1.10Keywords:
Degenerate metric, Kenmotsu manifold, CR-submanifoldAbstract
In this paper, we introduce screen transversal lightlike submanifolds of indefinite Kenmotsu manifolds. We obtain a characterization of screen transversal anti-invariant lightlike submanifolds as well as a condition for induced connection to be a metric connection and provide an example of $ST$-anti-invariant lightlike submanifold of $R^{9}_{2}$. Also, we obtain necessary and sufficient conditions for radical screen transversal lightlike submanifolds to be totally geodesic.
2000 Mathematics Subject Classification. 53C15, 53C40, 53C50, 53D15
Downloads
References
B. Sahin, Transversal lightlike submanifolds of indefinite Kaehler manifolds, An. Univ. Vest Timis., Ser. Mat., XLIV1 (2006), 119–145.
B. Sahin, Screen transversal lightlike submanifolds of indefinite Kaehler manifolds, Chaos Solitons Fractals, 38 (2008), 1439–1448.
K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math J., 21 (1972), 93–103.
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.
K. L. Duggal and B. Sahin, Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 106 (1–2) (2005), 137–165.
K. L. Duggal and B. Sahin, Generalised Cauchy-Riemann lightlike submanifolds of indefinte Kaehler manifolds, Acta Math. Hungar., 112 (1–2) (2006), 107–130.
N. Aktan, On non existence of lightlike hypersurfaces of indefinite Kenmotsu space form, Turk. J. Math., 32 (2008), 1–13.
R. S. Gupta and A. Sharfuddin, Generalised Cauchy-Riemann lightlike submanifolds of indefinite Kenmotsu manifolds, Note Mat., 30 (2) (2010), 49–59 (to appear).
R. S. Gupta and A. Sharfuddin, Lightlike submanifolds of indefinite Kenmotsu manifolds, Int. J. Contemp. Math. Sci., 5 (9–12) (2010), 475–496.
R. S. Gupta and A. Sharfuddin, Slant lightlike submanifolds of indefinite Kenmotsu manifold, Turk. J. Math., 35 (2011), 115–127.
R. S. Gupta and A. Upadhyay, Screen slant lightlike submanifolds of indefinite Kenmotsu manifolds, Kyungpook Math. J., 50 (2) (2010), 267–279.
