Abstract
In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Cosymplectic manifold. We provide a nontrivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of \({R^{9}_{2}}\) and prove some characterization Theorems.
Similar content being viewed by others
References
Bejan C.L., Duggal K.L.: Global lightlike manifolds and harmonicity. Kodai Mathematical Journal 28, 131–145 (2005)
Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, 2002.
Chen B.Y.: Geometry of Slant Submanifolds. Katholieke Universiteit, Leuven (1990)
Chen B.Y.: Slant Immersions. Bull. Aust. Math. Soc. 41, 135–147 (1990)
Duggal, K. L. and Sahin, B.: Lightlike submanifolds of indefinite Sasakian manifolds, Int. J. of Math. Math. Sci., Article ID 57585, (2007) 21 pages.
Duggal, K. L. and Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, vol. 364 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands 1996.
Gupta, R. S., Haider, S. M. K., Sharfuddin, A.: Slant submanifolds in Cosymplectic Manifolds, Colloquim Mathematicum, vol. 105 (2006), 207–219.
Kang T.H., Kim S.K.: Lightlike hypersurfaces of indefinite Cosymplectic manifolds. International Mathematical Forum 2, 3303–3316 (2007)
Lotta A.: Slant submanifolds in contact geometry. Bull. Math. Soc. Roumanie 39, 183–198 (1996)
Sahin B.: Slant lightlike submanifolds of indefinite Hermitian manifolds. Balkan Journal of Geometry and Its Applications 13, 107–119 (2008)
Yano, K. and Kon, M.: Structures on Manifolds, vol. 3 of Series in Pure Mathematics, World Scientific, Singapore, 1984.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gupta, R.S., Upadhyay, A. & Sharfuddin, A. Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds. Mediterr. J. Math. 8, 215–227 (2011). https://doi.org/10.1007/s00009-010-0077-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-010-0077-5