Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds

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Published: Jun 30, 2015
DOI: https://doi.org/10.5556/j.tkjm.46.2015.1727
Keywords:
Slant lightlike submanifold totally contact umbilical lightlike submanifolds totally contact geodesic lightlike submanifolds indefinite Kenmotsu manifolds

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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.

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How to Cite
Schdeva, R., Kumar, R., & Bhatia, S. S. (2015). Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds. Tamkang Journal of Mathematics, 46(2), 179–191. https://doi.org/10.5556/j.tkjm.46.2015.1727
Issue
Vol. 46 No. 2 (2015)
Section
Papers
Author Biographies

Rashmi Schdeva

School ofMathematics and Computer Applications, Thapar University, Patiala, India.

Rakesh Kumar

Department of Basic and Applied Sciences, Punjabi University, Patiala, India.

Satvinder Singh Bhatia

School ofMathematics and Computer Applications, Thapar University, Patiala, India.

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.