Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds

Rashmi Schdeva, Rakesh Kumar, Satvinder Singh Bhatia

Abstract


In this paper, we study totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds. We prove that there does not exist totally contact umbilical proper slant lightlike submanifold in indefinite Kenmotsu manifolds other than totally contact geodesic proper slant lightlike submanifold. We also prove that there does not exist totally contact umbilical proper slant lightlike submanifold of indefinite Kenmotsu space forms. Finally, we give some characterization theorems on minimal slant lightlike submanifolds of indefinite Kenmotsu manifolds.

Keywords


Slant lightlike submanifold, totally contact umbilical lightlike submanifolds, totally contact geodesic lightlike submanifolds, indefinite Kenmotsu manifolds

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References


C. L. Bejan and K. L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J., 28(2005), 131--145.

D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, New York, Birkhauser, 2002.

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

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

B. Y. Chen, Slant Immersions, Bull. Austral. Math. Soc., 41(1990), 135--147.

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

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

K. L. Duggal and B. Sahin, Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 106(2005), 125--153.

R. S. Gupta and A. Sharfuddin, Slant lightlike submanifolds of indefinite Kenmotsu manifolds, Turk J. Math., 35(2011), 115--127.

K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93--103.

A. Lotta, Slant submanifolds in contact geometry, Bull. Soc. Sci. Math. Roumanie., 39(1996), 183--198.

B. O'Neill, Semi-Riemannian Geometry with applications to relativity, New York, Academic Press, 1983.

B. Sahin, Slant lightlike submanifolds of indefinite Hermitian manifolds, Balkan J. Geom. Appl., 13(2008), 107--119.

K. Yano and M. Kon, Stuctures on Manifolds. Vol. 3 of Series in Pure Mathematics, Singapore, World Scientific, 1984.




DOI: http://dx.doi.org/10.5556/j.tkjm.46.2015.1727

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