A note on pointwise quasi hemi-slant submersions

Year 2025, Volume: 74 Issue: 2, 200 - 209, 19.06.2025

Sushil Kumar , Rajendra Prasad , Abdul Haseeb , Punit Kumar Sıngh

https://doi.org/10.31801/cfsuasmas.1545937

https://izlik.org/JA95XH72YB

Abstract

As a generalization of hemi-slant and semi-slant submersions, we discuss pointwise quasi Hemi-slant (PQHS) submersions from almost Hermitian manifolds onto Riemannian manifolds. We obtain various results satisfied by these submersions from Kähler manifolds onto Riemannian manifolds. Moreover, we find necessary and sufficient conditions on integrability of the distributions, and explore the geometry of totally geodesic foliations of discussed submersions. At last, we construct some examples of a PQHS submersion from an almost Hermitian manifold onto a Riemannian manifold.

Keywords

Hermitian manifolds , Riemannian submersions , pointwise quasi hemi-slant submersions

References

• Ali, S., Fatima, T., Generic Riemannian submersions, Tamkang J. Math., 44(4) (2013), 395-409. https://doi.org/10.5556/j.tkjm.44.2013.1211.
• Baird, P., Wood, J. C., Harmonic Morphism between Riemannian Manifolds, London Math. Soc. Monogr. New Series, 29, Oxford Univ. Press, Oxford, 2003. https://doi.org/10.1093/acprof:oso/9780198503620.001.0001.
• Chinea, D., Almost contact metric submersions, Rend. Circ. Mat. Palermo., 34 (1985), 89-104. https://doi.org/10. 1007/BF02844887.
• Falcitelli, M., Pastore, A. M., Ianus, S., Riemannian Submersions and Related Topics, World Scientific, 2004. https://doi.org/10.1142/5568.
• Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-738.
• Gündüzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, Demonstratio, 49(3) (2016), 345-356. https://doi.org/10.1515/dema-2016-0029.
• Gündüzalp, Y., Slant submersions from almost product Riemannian manifolds, Turk. J. Math., 37 (2013), 863-873. https://doi.org/10.3906/mat-1205-64.
• Ianus, S., Ionescu, A. M., Mocanu, R., Vilcu, G. E., Riemannian submersions from Almost contact metric manifolds, Abh. Math. Semin. Univ. Humbg., 81 (2011), 101-114. https://doi.org/10.1007/s12188-011-0049-0.
• Kumar S., Rai A. K., Prasad R., Pointwise slant submersions from Kenmotsu manifolds into Riemannian manifolds, Ital. J. Pure Appl. Math., 38 (2017), 561–572.
• Kumar S., Prasad R., Pointwise slant submersions from Sasakian manifolds, J. Math. Comput. Sci., 8(3) (2018), 454-466. https://doi.org/10.28919/jmcs/3684.
• Kumar, S., Prasad, R., Haseeb, A., Conformal semi-slant submersions from Sasakian manifolds, J. Anal , 31 (2023), 1855-1872. https://doi.org/10.1007/s41478-022-00540-9.
• Kumar S., Prasad R. Verma S. K., Hemi-slant Riemannian submersions from cosymplectic manifolds, Advanced Studies: Euro-Tbilisi Mathematical Journal, 15(4) (2022), 11-27. https://doi.org/10.32513/asetmj/19322008228.
• Lee, J. W., Sahin, B., Pointwise slant submersions, Bull. Korean Math. Soc., 51 (2014), 1115-1126. http://dx.doi. org/10.4134/BKMS.2014.51.4.1115.
• Noyan, E. B., Gündüzalp, Y., Proper bi-slant pseudo-Riemannian submersions whose total manifolds are in para-Kaehler manifolds, Honam Mathematical Journal, 44(3) (2022), 370-383. https://doi.org/10.5831/HMJ.2022.44.3.370.
• Noyan, E. B., Gündüzalp, Y., Proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry, International Electronic Journal of Geometry, 15(2) (2022), 253-265. https://doi.org/10.36890/iejg.1033345.
• Noyan, E. B., Gündüzalp, Y., Quasi hemi-slant pseudo-Riemannian submersions in para-complex geometry, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 72(4) (2023), 959-975. https://doi.org/10.31801/cfsuasmas.1089389.
• O’Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13(4) (1966), 458-469. https://doi.org/10. 1307/mmj/1028999604.
• Park, K. S., Prasad, R., Semi-slant submersions, Bull. Korean Math. Soc., 50(3) (2013), 951-962. http://dx.doi.org/ http://doi.org/10.4134/BKMS.2012.49.2.329.
• Prasad, R., Haseeb, A., Gupta, P., Quasi hemi-slant submanifolds of Kenmotsu manifolds, J. Appl. Math. & Informatics, 40(3-4) (2022), 475-490. https://doi.org/10.14317/jami.2022.475.
• Prasad R., Singh P. K., Kumar S., On quasi bi-slant submersions from Sasakian manifolds onto Riemannian manifolds, Afrika Matematika, 32(3-4) (2021), 403-417. https://doi.org/10.1007/s13370-020-00833-x.
• Prasad R., Singh P. K., Kumar S., Conformal semi-slant submersions from Lorentzian para Kenmotsu manifolds, Tbilisi Mathematical Journal, 14(1) (2021), 191-209. https://doi.org/10.32513/tmj/19322008115.
• Sahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math., 8(3) (2010), 437-447. https://doi.org/10.2478/s11533-010-0023-6.
• Sahin, B., Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull., 56(1) (2013), 173-183. https://doi.org/10.4153/CMB-2011-144-8.
• Sahin, B., Slant submersions from Almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roum., 54(102) (2011), 93-105.
• Sahin, B., Riemannian submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier, Academic Press, London, 2017.
• Sayar, C., Özdemir, F., Tastan, H. M., Pointwise semi-slant submersions whose total manifolds are locally product Riemannian manifolds, Int. J. Maps Math., 1(1) (2018), 91-115.
• Sepet S. A., Bozok H. G., Pointwise semi-slant submersion, Differential Geometry-Dynamical Systems, 22 (2020), 1-10.
• Sepet S. A., Ergüt M., Pointwise slant submersions from cosymplectic manifolds, Turkish Journal of Mathematics, 40(3) (2016), 582-93. https://doi.org/10.3906/mat-1503-98.
• Tastan, H. M., Sahin, B., Yanan, S., Hemi-slant submersions, Mediterr. J. Math., 13(4) (2016), 2171-2184. http: //dx.doi.org/https://doi.org/10.1007/s00009-015-0602-7.
• Watson, B., Almost Hermitian submersions, J. Differ. Geom., 11(1) (1976), 147-165. https://doi.org/10.4310/jdg/ 1214433303.
• Yano, K., Kon, M., Structures on Manifolds, World Scientific, Singapore, 1984. https://doi.org/10.1142/0067.