Pointwise Semi-Slant Warped Product Submanifold in a Lorentzian Paracosymplectic Manifold

TL;DR

This paper introduces and characterizes a new class of pointwise semi-slant warped product submanifolds in Lorentzian paracosymplectic manifolds, demonstrating their existence contrary to previous non-existence results for semi-slant warped products.

Contribution

It defines pointwise semi-slant submanifolds, provides lemmas, and proves the existence of non-trivial warped product submanifolds in Lorentzian paracosymplectic manifolds.

Findings

Existence of non-trivial pointwise semi-slant warped product submanifolds.

Characterization theorems for these submanifolds.

Counterexample to previous non-existence results.

Abstract

Recently Y{\"u}ksel et. al. \cite{SY} shows that there doesn't exist any proper semi-slant warped product submanifolds in a Lorentzian paracosymplectic manifold. In the present article, we first define and give preparatory lemmas for a new generalize class of semi-slant submanifolds called pointwise semi-slant submanifolds in a Lorentzian paracosymplectic manifold, and then we ensure by presenting some existence results and characterization theorem that there exist a non-trivial pointwise semi-slant warped product submanifolds in a Lorentzian paracosymplectic manifold counter to warped product semi-slant submanifolds in a Lorentzian paracosymplectic manifold.