Characterization of warped product submanifolds of Lorentzian concircular structure Manifolds

TL;DR

This paper characterizes warped product submanifolds within Lorentzian concircular structure manifolds, extending previous studies on contact CR-warped products and pseudo-slant submanifolds, and shows non-existence results for certain types.

Contribution

It provides new characterizations for contact CR-warped and pseudo-slant warped product submanifolds and proves the non-existence of proper warped product bi-slant submanifolds in these manifolds.

Findings

Characterization of contact CR-warped product submanifolds

Characterization of warped product pseudo-slant submanifolds

Non-existence of proper warped product bi-slant submanifolds

Abstract

Recently Hui et al. (\cite{HAP}, \cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although we constructed an example of a bi-slant submanifold of $(LCS)_n$-manifold.