Pointwise slant submanifolds and their warped products in Sasakian manifolds

Abstract

Recently, B.-Y. Chen and O.J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. In this paper, first we study pointwise slant and pointwise pseudo-slant submanifolds of almost contact metric manifolds and then using this notion, we show that there exist a non-trivial class of warped product pointwise pseudo-slant submanifolds of Sasakian manifolds by giving some useful results, including a characterization.

Warped Product Pointwise Semi Slant Submanifolds of Sasakian Space Forms and their Applications

“…A step forward, Park [12] extended the notion of pointwise slant submanifolds in the setting of AC-metric manifolds. Recently, Uddin and Al-Khalidi [24] modified the definition of pointwise slant submanifolds for ACmetric manifolds. More precisely, a submanifold M of an AC-metric manifold M is referred to as poinwise slant submanifold if ∀Y ∈ T y M such that η ∈ TM the angle θðYÞ between ΨY and T y M − f0g is independent of the choice of nonzero vector field Y ∈ T p M − f0g.…”

Warped product pointwise semi-slant submanifolds of cosymplectic space forms and their applications

“…A step forward, K. S. Park [12] extended the concept of pointwise slant submanifolds in almost contact metric manifolds. Recently, Uddin and Al-Khalidi [25] modified the definition of pointwise slant submanifolds for almost contact metric manifolds. More precisely, a submanifold M of an almost contact metric manifold M is said to be pointwise slant submanifold if for any X ∈ T x M such that η is tangential to M, the angle θðX Þ between Ψ X and T x M − f0g is independent of the choice of non zero vector field X ∈ T p M − f0g.…”

Geometry of warped product pointwise submanifolds of Sasakian manifolds

“…where BN and CN are the tangential and normal components of ϕN, respectively. Now, let us recall some basic facts of pointwise slant submanifolds of almost contact manifolds from [15] and [27] before we start to study on our main parts of the present paper.…”