Another class of warped product skew CR-submanifolds of Kenmotsu manifolds

2018/06/26 by Hui, Shyamal Kumar, Pal, Tanumoy, Roy, Joydeb
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.09800

Abstract

Recently, Naghi et al. \citeNAGHI studied warped product skew CR-submanifold of the form M₁×_fM_\bot of order 1 of a Kenmotsu manifold M such that M₁=M_T× M_θ, where M_T, M_\bot and M_θ are invariant, anti-invariant and proper slant submanifolds of M. The present paper deals with the study of warped product submanifolds by interchanging the two factors M_T and M_\bot, i.e, the warped products of the form M₂×_fM_T such that M₂=M_\bot× M_θ. The existence of such warped product is ensured by an example and then we characterize such warped product submanifold. A lower bounds of the square norm of second fundamental form is derived with sharp relation, whose equality case is also considered.

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