Sequential warped product submanifolds in locally product Riemannian manifolds

Abstract

In this paper, wepresent sequential warped product submanifolds of locally product Riemannian manifolds and show that there exists a class of non-trivial sequential warped product submanifolds of a locally product Riemannian manifold of the form (M? ??1 M?)??2 MT by giving non-trivial examples. Also, we prove some useful results for such warped products and establish Chen?s inequality which represents a relationship between the squared norm of the second fundamental form for the warping functions ?1 and ?2. Further, some applications of our main result are given.