Geometry of warped product pointwise semi-slant submanifolds of Kaehler manifolds

Abstract

In this paper, we study warped product pointwise semi-slant submanifolds of a Kaehler manifold. First, we prove some characterizations results in terms of the tensor fields T and F and then, we obtain a geometric inequality for the second fundamental form in terms of intrinsic invariants. Furthermore, the equality case is also discussed. Moreover, we give some applications for Riemannian and compact Remannian submanifolds as well, i.e., we construct necessary and sufficient conditions for the non-existence of compact warped product pointwise semi-slant submanifold in complex space forms.

Geometric classification of warped products isometrically immersed into Sasakian space forms

“…Proof. The proof is similar to the proof of Theorem 5.1 from in [3] for warped product pointwise semi-slant submanifolds of Kähler manifolds and for contact version in [35]. □ where and are the dimensions of the invariant and the pointwise slant submanifold , respectively, and = ln .…”

“…Proof We skip the proof of the above proposition due to similarity to the proof of Lemma 5.2 in for warped product pointwise semi‐slant submanifolds in a Kähler manifold. …”

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

“…Inspired by the research in [6,34] and using the Remark 3 in Theorem 2 for pointwise semi-slant warped product submanifolds, we obtained:…”

“…The role of immersibility and non-immersibility in studying the submanifolds geometry of a Riemannian manifold was affected by the pioneering work of the Nash embedding theorem [1], where every Riemannian manifold realizes an isometric immersion into a Euclidean space of sufficiently high codimension. This becomes a very useful object for the submanifolds theory, and was taken up by several authors (for instance, see [2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Its main purpose was considered to be how Riemannian manifolds could always be treated as Riemannian submanifolds of Euclidean spaces.…”

The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds

“…The work of Chen is about the characterization of CR-warped products in Kaehler manifolds, and derives the inequality for the second fundamental form. In fact, distinct classes of warped product submanifolds of the different kinds of structures were studied by several geometers (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Recently, Ali et al [15], established general inequalities for warped product pseudo-slants isometrically immersed in nearly Kenmotsu manifolds for mixed, totally geodesic submanifolds.…”