SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 3

Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold

Ali H. Alkhaldi(King Khalid University)
Akram Ali(King Khalid University)0000-0002-6053-3031
Mehmet Akif Akyol(BINGOL UNIVERSITY)0000-0003-2334-6955
Pages
—
Publication Date
2021-06-07
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we provide necessary and sufficient conditions that satisfy inequalities' equalities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this paper is to provide the complete classifications of the second fundamental form inequality for a warped product pointwise semi-slant submanifold in a Kaehler manifold which was obtained by Şahin [Th. 5.2, Warped product pointwise semi-slant submanifold of Kaehler manifold, Port.
📊
Key Findings & Data:Math. 2013] in terms of intrinsic and extrinsic invariants.
💡
Conclusion & Impact:Finally, we provide necessary and sufficient conditions that satisfy inequalities' equalities.
🔬Design:Research Article
📍Scope:2013 Verileri
⚙️Variables:CR-warped product · warped product · pointwise semi-slant submanifold

Abstract

The purpose of this paper is to provide the complete classifications of the second fundamental form inequality for a warped product pointwise semi-slant submanifold in a Kaehler manifold which was obtained by Şahin [Th. 5.2, Warped product pointwise semi-slant submanifold of Kaehler manifold, Port. Math. 2013] in terms of intrinsic and extrinsic invariants. In this paper, we give some conditions that are not addressed or considered in the cited paper mentioned above. Finally, we provide necessary and sufficient conditions that satisfy inequalities' equalities.

🔖

Cite This Article

Alkhaldi, A. H., Ali, A., Akyol, M. A. (2021). Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 3. https://doi.org/10.15672/hujms.585465

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. A. Ali, and P. Laurian-Ioan, Geometry of warped product immersion of Kenmotsu space forms and its application to slant immersions, J. Geom. Phy. 114, 276-290, 2017.
  2. A. Ali and P. Laurian-Ioan, Geometric classification of warped products isometrically immersed into Sasakian space forms, Math. Nachr. 292, 234–251, 2019.
  3. A. Ali, and C. Özel, Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications, Int. J. Geom. Methods Mod. Phys. 14, 1750042, 2017.
  4. A. Ali, S. Uddin, and W.A.M. Othman, Geometry of warped product pointwise semislant submanifolds of Kaehler manifolds, Filomat 32 (12), 3771-3788, 2017.
  5. R.L. Bishop, and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145, 1-9, 1969.
  6. O. Calin and D.C. Chang, Geometric mechanics on Riemannian manifolds: applications to partial differential equations, Springer Science & Business Media, 2006.
  7. B.-Y. Chen, Geometry of warped product CR-submanifold in Kaehler manifolds I, Monatsh. Math. 133, 177-195, 2001.
  8. B.-Y. Chen, Another general inequality for warped product CR-warped product submanifold in complex space forms, Hokkaido Math. J. 32, 415-444, 2003.
  9. B.-Y. Chen, and O. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turkish J. Math. 36, 630-640, 2012.
  10. F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen 53, 217-223, 1998.
  11. A. Mustafa, Geometry of warped product submanifolds of Riemannian manifolds, PhD thesis, University of Malaya, 2016.
  12. J. Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. 63, 2063, 1956.
  13. N. Papaghiuc, Semi-slant submanifold of Kaehler manifold, An. St. Univ. Al. I. Cuza. Iasi. 40, 55-61, 1994.
  14. B. Şahin, Non-existence of warped product semi-slant submanifolds of Kaehler manifolds, Geom. Dedicata 117, 95202, 2006.
  15. B. Şahin, Warped product pointwise semi-slant submanifold of Kaehler manifold, Port. Math. 70, 251-268, 2013.
  16. M.M. Tripathi, Improved Chen-Ricci inequality for curvature-like tensors and its applications, Diff. Geom. Appl. 29, 685-698, 2011.
  17. M. M. Tripathi, C-totally real warped product submanifolds, An. St. Univ. Al. I. Cuza. Iasi 58 (2), 417-436, 2012.
  18. B. Ünal, Multiply Warped Products, J. Geom. Phy. 34 (3-4), 287-301, 2000.
  19. K. Yano and M. Kon, Structures on manifolds, World Scientific, 1984.