TY  - JOUR
T1  - Submersions of hemi-slant submanifolds
AU  - Şahin, Bayram
AU  - Polat, Gülistan
AU  - Levent, Akın
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.15672/hujms.1534584
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1783
EP  - 1791
VL  - 54
IS  - 5
LA  - en
AB  - In this paper, we introduce   Riemannian submersions of  a hemi-slant submanifold of a Kähler manifold by observing the integrability of the anti-invariant distribution of  a hemi-slant submanifold and the integrability of the vertical distribution of a Riemannian submersion. Using this notion, we show that the base manifold is  a Kähler manifold in the submersion of a hemi-Kaehlerian slant submanifold of an almost Hermitian manifold. We obtain an inequality between the sectional curvature of the hemi-Kaehlerian slant submanifold and the holomorphic sectional curvature of the base manifold. If this inequality becomes equality, a geometric result is given. In addition, the Ricci tensor field on the horizontal distribution along this submersion is also found.
KW  - Kähler manifold
KW  - Riemannian submersion
KW  - hemi-slant submanifold
KW  - CR-submanifold
KW  - holomorphic sectional curvature
CR  - [1] A. Bejancu, Submanifolds of a Kähler manifold I, Proc. Amer. Math. Soc. 69 (1),
135–142, 1978.
CR  - [2] A. Carriazo, Bi-slant immersions, in: Proc. ICRAMS 2000, Kharagpur, India, 88–97,
2000.
CR  - [3] B. Y. Chen, CR-submanifolds of a Kähler manifold I, J. Dif. Geo. 16 (2), 305–322,
1981.
CR  - [4] B. Y. Chen, Differential geometry of real submanifolds in a Kähler manifold, Monatshefte
für Math. 91 (4), 257–274, 1981.
CR  - [5] S. Deshmukh, S. Ali and S.I. Husain, Submersions of CR-submanifolds of a Kaehler
manifold, Indian J. Pure Appl. Math. 19 (12), 1185–1205, 1988.
CR  - [6] S. Deshmukh, T. Ghazal and H. Hashem, Submersions of CR-submanifolds on an
almost Hermitian manifold, Yokohama Math. J. 40 (1), 45–57, 1992.
CR  - [7] T. Fatima, M. A. Akyol and A. A. Alzulaibani, On a submersion of generic submanifold
of a nearly Kaehler manifold, Int. J. Geom. Methods Mod. Phys. 19 (4),
2022.
CR  - [8] T. Fatima and S. Ali, Submersions of generic submanifolds of a Kaehler manifold,
Arab J. Math. Sci. 20 (1), 119–131, 2014.
CR  - [9] S. Kobayashi, Submersions of CR submanifolds, Tohoku Math. J. 39 (1), 95–100,
1987.
CR  - [10] J. Mikes, A. Vanzurova, and I. Hinterleitner, Geodesic Mappings and Some Generalizations,
Publ. Palacky University Olomouc, 2009.
CR  - [11] B. O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (4),
459–469, 1966.
CR  - [12] M. H. Shahid, F. R. Al-Solamy and M. Jamali, Submersions of CR Submanifolds, in:
Geometry of Cauchy-Riemann Submanifolds, 311–342, Springer-Verlag, Berlin, 2016.
CR  - [13] M.D. Siddiqi, Submersions of contact CR-submanifolds of generalized quasi-Sasakian
manifolds, J. Dyn. Syst. Geom. Theor. 18 (1), 81–95, 2020.
CR  - [14] B. Sahin, Warped product submanifolds of Kaehler manifolds with a slant factor, Ann.
Polon. Math. 95 (3), 207–226, 2009.
UR  - https://doi.org/10.15672/hujms.1534584
L1  - https://dergipark.org.tr/en/download/article-file/4151096
ER  -