Warped Product Pointwise Quasi Bi-slant Submanifolds of Kaehler Manifolds

Abstract

In this paper, we have examined the idea of warped product pointwise quasi bi-slant submanifolds in Kaehler manifolds. We have shown that every warped product pointwise quasi bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped product pointwise quasi hemi slant submanifold. Furthermore, we offer examples of both cases.

Keywords

• Quasi bi-slant submanifolds
• pointwise bi-slant submanifolds
• warped products

References

1. Akyol, M. A., Beyendi, S., Fatima, T., Ali, A.: On pointwise quasi bi-slant submanifolds. Filomat. 36(19), 6687-6697 (2022).
2. Al-Solamy, F. R., Khan, V. A., Uddin, S.: Geometry of warped product semi-slant submanifolds of nearly Kaehler manifolds. Results in Mathematics. 71(3), 783-799 (2017).
3. Beyendi, S., Akyol, M. A., Stankovic, M. S.: Pointwise quasi hemi-slant submanifolds. Filomat. 37(1), 127-138 (2023).
4. Bishop, R. L., O’Neill, B.: Manifolds of negative curvature. Trans. Am. Math. Soc. 145, 1-49 (1969).
5. Bejancu, A.: Semi-invariant submanifolds of locally product Riemannian manifolds. An. Univ. Timisoara. Ser Stiint. Math. 22, 3-11 (1984).
6. Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M.: Semi-Slant submanifolds of a Sasakian manifold. Geom. Dedicata. 78(2), 183-199 (1999).
7. Chen, B. Y.: Slant immersions. Bull. Aust, Math. Soc. 41(1), 135-147 (1990).
8. Chen, B. Y.: Geometry of slant submanifolds. Katholieke Universiteit Leuven. (1990).

9. Chen, B. Y.: Geometry of warped product CR-submanifolds in Kaehler manifolds. Monatsh. Math. 133, 177-195 (2001).
10. Chen, B. Y.: Geometry of warped product CR-submanifolds in Kaehler manifolds II. Monatsh. Math. 134, 103-119 (2001).
11. Chen, B. Y.: Another general inequality for CR-warped products in complex space forms. Hokkaido Math. J. 32(2), 415-444 (2003).
12. Chen, B. Y.: CR-warped products in complex projective spaces with compact holomorphic factor. Monatshefte für Mathematik. 141(3), 177-186 (2004).
13. Chen, B. Y., Garay, O. J.: Pointwise slant submanifolds in almost Hermitian manifolds. Turk. J. Math. 36, 630-640 (2012).
14. Chen, B. Y.: Geometry of warped product submanifolds: A survey. J. Adv. Math. Stud. 6(2), 1-8 (2013).
15. Chen, B. Y.: Differential geometry of warped product manifolds and submanifolds. World Scientific. (2017).
16. Chen, B. Y., Uddin, S.: Warped product pointwise bi-slant submanifolds of Kaehler manifolds. Publicationes Mathematicae. 92(1-2), 183-199 (2018).
17. Chen, B. Y., Shahid, M. H., Al-Solamy, F. R.: Complex Geometry of Slant Submanifolds. Springer. Berlin (2021).
18. Chen, B. Y., Shahid, M. H., Al-Solamy, F. R.: Contact Geometry of Slant Submanifolds. Springer. Berlin (2021).
19. Etayo, F.: On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debrecen. 53(1-2), 217-223 (1998).
20. Khan, V. A., Khan, M. A.: Semi-slant submanifolds of a nearly Kaehler manifold. Turk. J. Math. 31(4), 341-353 (2007).
21. Kon, M.: Remarks on anti-invariant submanifolds of a Sasakian manifold. Tensor (N.S.). 30, 239-245 (1976).
22. Lone, M. A., Shahid, M. H., Sharma, S. D.: Hemi-slant submanifolds of nearly Kaehler manifolds. Gulf Journal of Mathematics. 4(3), (2016).
23. Lone, M. A., Majeed, P.: Warped Product Quasi Bi-Slant Submanifolds of Kaehler Manifolds Lobachevskii Journal of Mathematics. 45(2), 718-727 (2024).
24. Lone, M. A., Majeed, P.: An optimized Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms. Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science. 123-138 (2024).
25. Majeed, P., Lone, M. A.: Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics. 1-13 (2023).
26. Naghi, M. F., Stankovic, M. S., Alghamdi, F.: Chen’s improved inequality for pointwise hemi-slant warped products in Kaehler manifolds. Filomat. 34(3), 807-814 (2020).
27. Papaghuic, N.: Semi-slant submanifolds of a Kahlerian manifold. An. Stiint. Univ. Al. I. Cuza Iasi Mat. 40(1), 55-61 (1994).
28. Prasad, R., Shukla, S., Haseeb, A., Kumar, S.: Quasi hemi-slant submanifolds of Kaehler manifolds. Honam Mathematical Journal. 42(4), 795-809 (2020).
29. Prasad, R., Akyol, M. A., Verma, A. K., Kumar, S.: Quasi Bi-Slant Submanifolds of Kaehler Manifolds. International Electronic Journal of Geometry. 15(1), 57-68 (2022).
30. Şahin, B.: Warped product submanifolds of Kaehler manifolds with a slant factor. Ann. Polon. Math. 95(3), 207-226 (2009).
31. Şahin, B.: Non-existence of warped product semi-slant submanifolds of Kaehler manifolds. Geometriae Dedicata. 117(1), 195-202 (2006).
32. Şahin, B.: Warped product pointwise semi-slant submanifolds of Kaehler manifolds. Port. Math. 70, 252-268 (2013).
33. 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).