Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Year 2022, Volume: 15 Issue: 1, 57 - 68, 30.04.2022

Rajendra Prasad , Mehmet Akif Akyol , Sandeep Kumar Verma , Sumeet Kumar

https://doi.org/10.36890/iejg.1061786

Cited By: 4

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.

Keywords

Quasi bi-slant submanifold, Kaehler manifold, totally geodesic, distribution

References

• [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.