POINTWISE QUASI HEMI-SLANT SUBMANIFOLDS OF COSYMPLECTIC MANIFOLDS

Abstract

The object of this manuscript is to investigate related to the geometry of distributions on pointwise quasi hemi-slant submanifolds (abbr. pqhs) in cosymplectic manifolds. In this context, the preconditions for such distributions to be integrable, totally geodesic foliation, totally geodesic and mixed totally geodesic are obtained. In addition to, we are going to present several examples to guarantee these new types of submanifolds in cosymplectic manifolds.

Keywords

• Pointwise quasi hemi-slant
• cosymplectic manifold
• totally geodesic foliation
• totally geodesic
• mixed totally geodesic.

References

1. Lie S. Geometrie der Berührungstransfor-mationen. B. G. Teubner, Leipzig. 1896.
2. Blair DE and Goldber SI. Topology of almost contact manifolds. J. Differential Geom. 1967;1:347-354.
3. Ludden GD. Submanifolds of cosymplectic manifolds. J. Differential Geom. 1970;4:237-244.
4. Cabras A, Ianus S and Pitis GH. Extrinsic spheres and parallel submanifolds in cosymplectic manifolds. Toyama Math. J. 1994;17:31-53.
5. Chen BY. Slant immersions. Bull. Aust. Math. Soc. 1990;41(1):135-147.
6. Cabrerizo JL, Carriazo A, Fernandez LM and Fernandez M. Semi-slant submanifolds of a Sasakian manifold. Geom. Dedicata. 1999;78(2):183-199.
7. Chen BY. Geometry of slant submanifolds. Katholieke Universiteit Leuven. 1990.
8. Lotta A. Slant submanifolds in contact geometry. Bull. Math. Soc. Sci. Math. Roumanie. 1996;39:183-198.

9. Matsumoto K, Mihai I, Tazawa Y. Ricci tensor of slant submanifolds in complex space forms. Kodai Math. J. 2003;26:85-94.
10. Şahin B. Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 2006;43(4):717-732.
11. Şahin B. Slant submanifolds of quaternion Kaehler manifolds. Commum. Korean Math. Soc. 2007;22(1):123-135.
12. Şahin B and Keleş S. Slant submanifolds of Kaehler product manifolds. Turkish J. Math. 2007;31(1):65-77
13. Taştan HM, Şahin B and Yanan Ş. Hemi-slant submanifolds. Mediterr. J. Math. 2016;13(4):2171-2184. Uddin S, Khan VA, Özel C. Classification of totally umbilical ξ^⊥ CR-submanifolds of cosymplectic manifolds. Rocky Mountain J. Math. 2015;45(1):361-369.
14. Akyol MA, Beyendi S, Fatima T and Ali A. Pointwise quasi bi-slant submanifolds. Filomat. 2022;36(19):6687-6697.
15. Beyendi S, Akyol MA, Stanković MS. Pointwise quasi hemi-slant submanifolds. Filomat. 2023;37(1):127-138.
16. Carriazo A. New developments in slant submanifolds theory. Narasa Publishing Hause New Delhi, India. 2002.
17. Chen BY and Uddin S. Warped product pointwise bi-slant submanifolds of Kaehler manifolds. Publ. Math. Debrecen. 2018;92(1-2):183-199.
18. Etayo F. On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debrecen. 1998;53:217-223.
19. Lone MA, Lone MS and Shahid MH. Hemi-slant submanifolds of cosymplectic manifolds. Cogent Math. 2016;3(1):120-143.
20. Papaghuic N. Semi-slant submanifold of Kaehlerian manifold. An. Ştiint. Univ. A1. I. Cuza. Iaşi. Math. (N.S.). 1994;9:55-61.
21. Prasad R, Verma SK and Kumar S. Quasi hemi-slant submanifolds of Sasakian manifolds. J. Math. Comput. Sci. 2020;10(2):418-435.
22. Prasad, R, Singh PK and Rai AK. On quasi hemi-slant submanifolds of nearly Kaehler manifolds. Differ. Geom. Dyn. Syst. 2021;23:188-202.
23. Prasad R, Verma SK, Kumar S and Chaubey SK. Quasi hemi-slant submanifolds of cosymplectic manifolds. Korean J. Math. 2020;28(2):257-273.
24. Prasad R, Shukla SS, Haseeb A and Kumar S. Quasi hemi-slant submanifolds of Kaehler manifolds. Honam Math. J. 2020;42(4);795-809.
25. Prasad R, Akyol MA, Singh PK, Kumar S. On quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds. Journal of Mathematical Extension. 2022;16(6):1-25.
26. Siddesha MS, Praveena MM and Bagewadi CS. On quasi hemi-slant submanifolds of LP-cosymplectic manifolds. Math., Anal., Appl. 2021;3(3):39-49.
27. Şahin B. Non-existence of warped product semi-slant submanifolds of Kaehler manifolds. Geom. Dedicata. 2006;117:195-202.
28. Uddin S, Chen BY and Al-Solamy FR. Warped product bi-slant immersions in Kaehler manifolds. Mediterr. J. Math. 2017;14(2):1-10.
29. Şahin B. Warped product pointwise semi-slant submanifolds of Kaehler manifolds. Port. Math. 2013;70(3):252-268.
30. Park KS. Pointwise slant and pointwise semi-slant submanifolds in almost contact metric manifolds. Mathematics. 2020;8(6):1-33.
31. Park KS. On the pointwise slant submanifolds. In Hermitian-Grassmannian Submanifolds. Suh, Y., Ohnita, Y., Zhou, J., Kim, B., Lee, H., Eds.; Springer Proceedings in Mathematics and Statistics. 203; Springer: Singapore. 2017.
32. Akyol MA and Beyendi S. A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1508-1521.
33. Perktaş SY, Blaga AM and Kılıç E. Almost bi-slant submanifolds of an almost contact metric manifold. J. Geom. 2021;112(2):1-23.
34. Blair DE. Contact manifolds in Riemannian geometry. Lecture Notes in Mathematic. Vol: 509, Springer-Verlag, Berlin. 1976.
35. Akyol MA. Conformal anti-invariant submersions from cosymplectic manifolds. Hacet. J. Math. Stat. 2017;46:177–192.
36. Blair DE. The theory of quasi-Sasakian structure. J. Differential Geom. 1. 1967;3(4):331-345.
37. Chen BY and Garay OJ. Pointwise slant submanifolds in almost Hermitian manifolds. Turkish J. Math. 2012;36(4):630-640.