Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds

Year 2025, Volume: 74 Issue: 1, 117 - 129, 08.03.2025

Sedat Ayaz , Yılmaz Gündüzalp

https://doi.org/10.31801/cfsuasmas.1506942

Abstract

In this article, firstly we study pointwise slant, pointwise hemi-slant submanifolds whose ambient spaces are para-cosymplectic manifolds and we prove that there exist pointwise hemi-slant nontrivial warped product submanifolds whose ambient spaces are para-cosymplectic manifolds by giving some examples. We get several theorems and some characterizations. Later, we also obtain some inequalities.

Keywords

Para-cosymplectic manifold , pointwise hemi-slant submanifold , warped product submanifold

References

• Alegre, P., Carriazo, A., Slant submanifolds of para Hermitian manifolds, Mediterr. J. Math., 14 (2017), 214-221. https://doi.org/10.1007/S00009-017-1018-3
• Ayaz, S., Gündüzalp, Y., Warped product pointwise hemi-slant submanifolds whose ambient spaces are nearly para-Kaehler manifolds, Turk. J. Math., 48(3) (2024), 477-497. https://doi.org/10.55730/1300-0098.3520
• Bishop, R. L., O’neill, B., Manifolds of negative curvature, Trans Amer. Math. Soc., 145 (1969), 1-9.
• Chen, B. Y., Garay, O. J., Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math., 36 (2012), 630-640.
• Gulbahar, M., Kılıç, E., Celik, S. S., Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math., 39 (2015), 884-899.
• Hiepko, S., Eine innere Kennzeichnung der verzeten Producte, Math. Ann., 241 (1979), 209-215. https://eudml.org/doc/163263
• Park, K. S., Pointwise slant and pointwise semi-slant submanifolds in almost contact metric manifolds, Mathematics, 13 (2020), 1-33.
• Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S., Quasi bi-slant submanifolds of Kaehler manifolds, International Electronic Journal of Geometry, 15(1) (2022), 57-68.
• Sahin, B., Warped product submanifolds Kaehler manifolds with a slant factor, Ann. Polon. Math., 95(3) (2009), 207-226. https://doi.org/10.4064/ap95-3-2
• Sato, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30(3) (1976), 219-224.
• Uddin, S., Khan, V. A., Khan, K. A., A note on warped product submanifolds of cosymplectic manifolds, Filomat, 24 (2010), 95-102.
• Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(1) (2009), 37-60.