Warped product CR-submanifolds of LP-cosymplectic manifolds

Abstract

In this paper, we study warped product CR-submanifolds of LP-cosymplectic manifolds. We have shown that the warped product of the type M = N T × f N ⊥ does not exist, where NT and N ⊥ are invariant and anti-invariant submanifolds of an LP-cosymplectic manifoldM , respectively. Also, we have obtained a characterization result for a CR-submanifold to be locally a CRwarped product.

Warped product bi-slant submanifolds of cosymplectic manifolds

“…Since M is proper, then cos 2 θ 2 0, thus from (20) we conclude that f is constant. Hence, the theorem is proved completely.…”

“…Warped product submanifolds have been studied rapidly and actively, since Chen introduced the notion of CR-warped products of Kaehler manifolds [10,11]. Different types of warped product submanifolds have been studied in several kinds of structures for last fifteen years (see [2,15,18,20,22]). The related studies on this topic can be found in Chen's book and a survey article [12,13].…”

“…Recently, warped product submanifolds of cosymplectic manifolds were studied in ( [1], [15], [20][21][22]). In this paper, we study warped product bi-slant submanifolds of cosymplectic manifolds.…”

Nonexistence of $$\mathcal {P}\mathcal {R}$$PR-semi-slant warped product submanifolds in paracosymplectic manifolds

“…Due to the non-definitive nature of the Riemannian metric, the geometry of warped product submanifolds with more general non-degenerate metric (i.e., positive as well as negative definite metric) became a topic of investigation. In light of that, many authors discussed the existence and nonexistence of such warped product submanifolds in Lorentzian settings [33,42]. Recently, Chen and Munteanu [13], the authors of [30,31] and Aydin and Cöken [2] initiated the study of the geometry of pseudo-Riemannian warped products submanifolds in para-Kähler manifolds, paracontact manifolds and slant submanifold in semi-Riemannian manifolds, respectively.…”

Warped product pseudo-slant submanifolds of (LCS)_n-manifolds

“…Again Atceken [2] studied warped product semi-slant submanifolds in Kenmotsu manifolds. Beside these, Uddin and his co-authors studied warped product submanifolds in different context such as ( [13], [28]) etc. Recently, Hui and Atceken [10] studied warped product semi-slant submanifolds of (LCS) n -manifolds.…”