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Journals / International Electronic Journal of Geometry / 2026 / Volume: 15 Issue: 1

Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Rajendra Prasad(Luknow University)0000-0002-7502-0239
Mehmet Akif Akyol(Bingöl University)0000-0003-2334-6955
Sandeep Kumar Verma(Lucknow university)0000-0003-2793-0120
Sumeet Kumar(Luknow University)0000-0003-1214-5701
Pages
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Publication Date
2022-04-30
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AI Summary & Key Takeaways

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

Finally, we obtain the necessary and sufficient conditions for a quasi bi-slant submanifold to be local product Riemannian manifold and also construct some examples of such submanifolds.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we introduce the new notion of quasi bi-slant submanifolds of almost Hermitian manifolds.
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Key Findings & Data:Necessary and sufficient conditions for the integrability of distributions which are involved in the definition of such submanifolds of a Kaehler manifold are obtained.
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Conclusion & Impact:Finally, we obtain the necessary and sufficient conditions for a quasi bi-slant submanifold to be local product Riemannian manifold and also construct some examples of such submanifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Quasi bi-slant submanifold · Kaehler manifold · totally geodesic

Abstract

In this paper, we introduce the new notion of quasi bi-slant submanifolds of almost Hermitian manifolds. Necessary and sufficient conditions for the integrability of distributions which are involved in the definition of such submanifolds of a Kaehler manifold are obtained. We also investigate the necessary and sufficient conditions for these submanifolds of Kaehler manifolds to be totally geodesic and study the geometry of foliations determined by the above distributions. Finally, we obtain the necessary and sufficient conditions for a quasi bi-slant submanifold to be local product Riemannian manifold and also construct some examples of such submanifolds.

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Cite This Article

Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S. (2022). Quasi Bi-Slant Submanifolds of Kaehler Manifolds. International Electronic Journal of Geometry, Volume: 15 Issue: 1. https://doi.org/10.36890/iejg.1061786

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References (22)

  1. Akyol, M. A., Beyendi, S.: A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69(2), 1508-1521, 2020.
  2. Al- solamy, F. R., Khan, M. A., Uddin, S.: Totally umbilical hemi-slant submanifolds of Kaehler manifolds. Abstr. Appl. Anal. Article ID 987157, 9 pages, (2011).
  3. Bagewadi, C.S., Nirmala, D., Siddesha, M. S.: Semi-invariant submanifolds of (LCS)N-manifold. Communications of the Korean Mathematical Society 33(4), 1331-1339 (2018).
  4. Benjancu, A., Papaghuic, N.: Semi-invariant Submanifolds of a Sasakian manifold. An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.) 27, 163-170 (1981).
  5. Blaga, A. M.: Invariant, anti-invariant and slant submanifolds of para-Kenmotsu manifold. BSG Publ. 24, 125-138 (2017).
  6. Blair, D. E.: Contact manifold in Riemannian geometry, Lecture notes in Math. 509, Springer-Verlag, New-York (1976).
  7. Cabrerizo, J. L., Carriazo, A., Fernandez, L.M., Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42, 125-138 (2000).
  8. Chen, B. Y.: Geometry of slant submanifolds, Katholieke Universiteit, Leuven (1990).
  9. Chen, B. Y.: Slant immersions. Bull. Austral. Math. Soc. 41(1), 135-147 (1990).
  10. Cortes, V., Mayer, C., Mohaupt, T., Saueres, F.: Special geometry of Euclidean supersymmetry 1. vector multiplets. J. High Energy Phys. 03-028 (2004).
  11. De, U. C., Shaikh, A. A.: Complex manifolds and Contact manifolds, Narosa Publ. House, 2009.
  12. Etayo, F.: On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debrecen 53, 217–223 (1998).
  13. Kon, M.: Remarks on anti-invariant submanifolds of a Sasakian manifold. Tensor (N.S.) 30, 239-245 (1976).
  14. Lotta, A.: Slant submanifold in contact geometry. Bull. Math. Soc. Romanie 39, 183-198 (1996).
  15. Papaghuic, N.: Semi-slant submanifold of Kaehlerian manifold. An. St. Univ. Al. I. Cuza. Iasi. Math.(N.S.) 9, 55-61 (1994).
  16. Perktaş, S. Y., Blaga, A. M., Kılıç, E.: Almost bi-slant submanifolds of an almost contact metric manifold. Journal of Geometry, 112(2), (2021).
  17. Şahin, B.: Warped product submanifolds of a Kaehler manifold with a slant factor. Ann. Pol. Math., 95, 107-126 (2009).
  18. Şahin, F.: Cohomology of hemi-slant submanifolds of a Kaehler manifolds. J. Adv. Studies Topology, 5, 27-31 (2014).
  19. Uddin, S., Chen, B. Y., Al-Solamy, F. R.: Warped product bi-slant immersions in Kaehler manifolds. Mediterr. J. Math. 14(2), 14-95 (2017).
  20. Tashiro, Y.: On contact structures of Hypersurfaces in Almost complex manifolds I. Tohoku Math. J., 15, 62-78 (1963).
  21. Taştan, H. M., Özdemir, F.: The geometry of hemi-slant submanifolds of a locally product Riemannian manifold. Turkish Journal of Mathematics, 39 268–284, (2015).
  22. Yano, K., Kon, M.: Structures on manifolds, World scientific, 1985.