Sequential Warped Product Submanifolds in Locally Product Riemannian Manifolds

Abstract

In this paper, we present  sequential warped products 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 $(M_{\theta}\times_{\sigma_{1} }M_{\perp})\times_{\sigma_{2}}M_{T }$ 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 $\sigma_1$ and $\sigma_2$ .Further, some applications of our main result are given.