Pointwise hemi-slant warped product submanifolds in nearly Kaehler manifolds

Lamia Saeed Alqahtani; Siraj Uddin; Rawan Bossly

doi:10.2478/auom-2025-0026

.blurhash-client-img { display: none !important; }

Pointwise hemi-slant warped product submanifolds in nearly Kaehler manifolds

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 33 (2025): Issue 3 (October 2025)

By: Lamia Saeed Alqahtani, Siraj Uddin and Rawan Bossly

Open Access

|Nov 2025

Abstract

In this paper, we introduce the notion of pointwise hemi-slant sub-manifolds of nearly Kaehler manifolds. Further, we study their warped products and prove the necessary and sufficient condition that a point-wise hemi-slant submanifold to be a warped product manifold. Also, we establish a sharp inequality for the pointwise hemi-slant warped product submanifolds of the form M = M_⊥ ×_f M_θ which is mixed totally geodesic in an arbitrary nearly Kaehler manifold ~M. The equality case is also discussed.

References

F. R. Al-Solamy, V. A. Khan, S. Uddin, Geometry of warped product semi-slant submanifolds of nearly Kaehler manifolds, Results. Math. 71 (3-4) (2016), 783–799.
Search in Google Scholar Back to article
R.L. Bishop, B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–49.
Search in Google Scholar Back to article
A. Carriazo, New developments in slant submanifolds theory, Narosa Publishing House, New Delhi, 2002.
Search in Google Scholar Back to article
B.-Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41 (1) (1990), 135–147.
Search in Google Scholar Back to article
B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Belgium, 1990.
Search in Google Scholar Back to article
B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133 (2001), 177–195.
Search in Google Scholar Back to article
B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math. 134 (2001), 103–119.
Search in Google Scholar Back to article
B.-Y. Chen, Differential geometry of warped product manifolds and sub-manifolds, World Scientific, Hackensack, NJ 2017.
Search in Google Scholar Back to article
B.-Y. Chen, S. Uddin, Slant geometry of warped products in Kaehler and nearly Kaehler manifolds,: Complex Geometry of Slant Submanifolds, 61–100, Springer, Singapore, 2022.
Search in Google Scholar Back to article
B.-Y. Chen, O. J. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math. 36 (2012), 630–640.
Search in Google Scholar Back to article
B.-Y. Chen, CR-warped product submanifolds in Kaehler manifolds: Geometry of Cauchy-Riemann submanifolds, 1–25, Springer, Singapore, 2016.
Search in Google Scholar Back to article
A. Gray, Nearly Kähler manifolds, J. Differential Geom. 4 (1970), 283–309.
Search in Google Scholar Back to article
A. Gray, The structure of nearly Kähler manifolds, Math. Ann. 223 (3) (1976), 233–248.
Search in Google Scholar Back to article
S. Hiepko, Eine inner kennzeichungder verzerrten produkte, Math. Ann. 241 (1979), 209-215.
Search in Google Scholar Back to article
I. Hasegawa, I Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102 (2003), 143–150.
Search in Google Scholar Back to article
A. Mihai, Warped product submanifolds in complex space forms, Acta Sci. Math. Szeged 20 (2004), 311–319.
Search in Google Scholar Back to article
B. O’Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
Search in Google Scholar Back to article
B. Sahin, Nonexistence of warped product semi-slant submanifolds of Kaehler manifolds, Geom. Dedicata 117 (2006), 195–202.
Search in Google Scholar Back to article
B. Sahin, Warped product submanifolds of Kaehler manifolds with a slant factor, Ann. Pol. Math. 95 (2009), 207–226.
Search in Google Scholar Back to article
B. Sahin, Warped product pointwise semi-slant submanifolds of Kaehler manifolds, Port. Math. 70 (2013), 252–268.
Search in Google Scholar Back to article
S. Uddin, F.R. Al-Solamy, K.A. Khan, Geometry of warped product pseudo-slant submanifolds in Kaehler manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 62 (2) (2016), 927–938.
Search in Google Scholar Back to article
S. Uddin, B.-Y. Chen, F.R. Al-Solamy, Warped product bi-slant immersions in Kaehler manifolds, Mediterr. J. Math. 14 (2) (2017), Art. 95, 11 pp.
Search in Google Scholar Back to article
S. Uddin, L.S. Alqahtani, A. A. Alkhaldi, F. Y. Mofarreh, CR-slant warped product submanifolds in nearly Kaehler manifolds, Int. J. Geom. Methods Mod. Phys. 17 (1) (2020), Art.2050003, 11 pp.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2025-0026 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 5 - 19

Submitted on: Sep 17, 2024

Accepted on: Apr 7, 2025

Published on: Nov 29, 2025

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Slant,

pointwise slant,

pointwise hemi-slant,

Warped products,

nearly Kaehler manifolds

Related subjects:

Mathematics,

General mathematics

© 2025 Lamia Saeed Alqahtani, Siraj Uddin, Rawan Bossly, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 3 (October 2025)