Pointwise Pseudo-slant Warped Product Submanifolds in a Kähler Manifold

Warped product submanifolds of Kaehler manifolds with pointwise slant fiber

“…In this paper, first we define pointwise hemi-slant submanifolds of Kaehler manifolds and then we show that there exists a class of non-trivial warped product submanifolds of the form M ⊥ × f M θ in a Kaehler manifold M such that M ⊥ and M θ are totally real and proper pointwise slant submanifolds of M, respectively. We note that one of the characterization result of such warped products is given in [18] by using different technique. It is also notice that the warped product hemi-slant submanifolds of almost Hermitian manifolds were studied under the name of warped product pseudo-slant submanifolds in [18][19][20].…”

“…We note that one of the characterization result of such warped products is given in [18] by using different technique. It is also notice that the warped product hemi-slant submanifolds of almost Hermitian manifolds were studied under the name of warped product pseudo-slant submanifolds in [18][19][20].…”

“…[18] Let M be a pointwise hemi-slant submanifold of a Kaehler manifold M. Then M is locally a warped product submanifold of the form M ⊥ × f M θ if and only ifA FPX V − A JV PX = V(µ) cos 2 θ X, ∀ X ∈ Γ(D θ ), V ∈ Γ(D ⊥ )…”

Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications

“…Furthermore, ∇ and ∆ are the gradient and the Laplacian operator on M n 1 1 , respectively, and H is the mean curvature vector of M n . This equally holds in (33) if, and only if, ϕ is a mixed, totally geodesic isometric immersion and the following satisfies…”

“…By using classifications of pointwise bi-slant submanifolds which were defined in [32], we derived similar inequalities for warped product pointwise pseudo-slant submanifolds [33], warped product pointwise semi-slant submanifolds [34], and CR-warped product submanifolds [17] in a complex space form as well.…”