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This article covers the geometric study of pointwise slant and pointwise semi-slant submanifolds of a para-Cosymplectic manifold M? 2m+1 with the semi-Riemannian metric. We give an advanced definition of these type of submanifolds for the spacelike and timelike vector fields. We obtain the characterization results for the involutive and totally geodesic foliation for such type of manifold M? 2m+1.

The main purpose of this paper is to study transversal hypersurface (briefly, $\mathcal{T}$-hypersurface) $P$ of a paraSasakian manifold $M$. We derive results allied with totally geodesic and totally umbilical $\mathcal{T}$-hypersurface of $M$. The necessary and sufficient condition for normality of $(\mathfrak{f},\mathfrak{g},\mu,\upsilon,\delta)$-structure is established. Examples of $\mathcal{T}$-hypersurface are also illustrated.

We generalize the study of pointwise slant lightlike submanifolds of indefinite cosymplectic manifold. We prove the existence of semi-Riemannian screen distribution when the rank of radical is less than the index of a manifold and give a generalized definition of pointwise slant lightlike submanifolds. Also, we have constructed examples showing timelike components in screen distribution and derived the condition for pointwise slant lightlike submanifolds, which helps to conclude various related results. We studied pointwise slant lightlike submanifolds under different conditions, like totally umbilical and minimal lightlike, and obtained results. Mathematical Subjclass Classfication(2020): 53C12, 53C25, 53B25, 53B30, 53D10.