Alqahtani, L.S.; Uddin, S.; Bossly, R. Warped Product Pointwise Hemi-Slant Submanifolds of Nearly Kaehler Manifolds. Preprints2023, 2023062023. https://doi.org/10.20944/preprints202306.2023.v1
APA Style
Alqahtani, L.S., Uddin, S., & Bossly, R. (2023). Warped Product Pointwise Hemi-Slant Submanifolds of Nearly Kaehler Manifolds. Preprints. https://doi.org/10.20944/preprints202306.2023.v1
Chicago/Turabian Style
Alqahtani, L.S., Siraj Uddin and Rawan Bossly. 2023 "Warped Product Pointwise Hemi-Slant Submanifolds of Nearly Kaehler Manifolds" Preprints. https://doi.org/10.20944/preprints202306.2023.v1
Abstract
In this paper, we introduce the notion of pointwise hemi-slant submanifolds of nearly Kaehler manifolds. Further, we study their warped products and prove the necessary and sufficient condition that a pointwise hemi-slant submanifold to be a warped product manifold. Also, we prove that every pointwise hemi-slant warped product submanifold $M=M_\perp\times_fM_\theta$ which is mixed totally geodesic in an arbitrary nearly Kaehler manifold $\tilde M$ satisfies $\|h\|^2\geq\frac{2p}{9}\cos^2\theta\|\nabla(\ln f)\|^2,$ where $\|h\|$ is the length of the second fundamental form of $M$ and $2p=\dim M_\theta$; while $\nabla(\ln f)$ is the gradient of $\ln f$ along $M_\perp$. The equality case of this inequality is also given.
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
