Czechoslovak Mathematical Journal, Vol. 63, No. 1, pp. 177-190, 2013

Slant and pseudo-slant submanifolds
in $ LCS$-manifolds

Mehmet Atçeken, Shyamal Kumar Hui

Mehmet Atçeken, Gaziosmanpasa University, Faculty of Arts and Sciences, Department of Mathematics, 60100 Tokat, Turkey, e-mail: mehmet_atceken@yahoo.com.tr; Shyamal Kumar Hui, Nikhil Banga Sikshan Mahavidyalaya, Bishnupur, 722 122 Bankura, West Bengal, India, e-mail: shyamal_hui@yahoo.co.in

Abstract: We show new results on when a pseudo-slant submanifold is a $ LCS$-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudo-slant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an $ LCS$-manifold to illustrate the subject.

Keywords: slant submanifold, pseudo-slant submanifold, $ LCS$-manifold

Classification (MSC 2010): 53C15, 53C25


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