Generic Submersions in Contact Geometry

Öz

In the present paper, we introduce a new type of Riemannian submersion in the contact framework such that the fibers of such submersion are generic submanifolds, as given in [10]. This type of submersion is a generalization of many kinds of submersion introduced before in the literature. Once the Reeb vector field \xi is tangent to the fibers, its position is given such that it should lie in the anti-invariant distribution D^0, which is given in the definition of the generic submersion. Moreover, we give an example and some results for such submersions.

Anahtar Kelimeler

• Riemannian submersion
• almost contact metric manifold
• distribution

Kaynakça

1. O'Neill B. The fundamental equations of a submersion. Michigan Mathematical Journal. 1966 Dec;13(4):459-69.
2. Gray A. Pseudo-Riemannian almost product manifolds and submersions. Journal of Mathematics and Mechanics. 1967 Jan 1;16(7):715-37.
3. Watson B. Almost hermitian submersions. Journal of Differential Geometry. 1976 Jan;11(1):147-65.
4. Prasad R, Akyol MA, Kumar S, Singh PK. Quasi bi-slant submersions in contact geometry. Cubo (Temuco). 2022 Apr;24(1):1-20.
5. Sari R, Akyol MA. Hemi-slant ξ⊥-Riemannian submersions in contact geometry. Filomat. 2020;34(11):3747-58.
6. Sahin B. Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications. Academic Press; 2017 Jan 23.
7. Pastore AM, Falcitelli M, Ianus S. Riemannian submersions and related topics. World Scientific; 2004 Jun 21.
8. Ronsse, G.B.: Generic and skew CR-submanifolds of a Kaehler manifold. Bull. Inst. Math. Acad. Sin. 18, 127–141 (1990)

9. Sayar C, Taṣtan HM, Özdemir F, Tripathi MM. Generic submersions from Kaehler manifolds. Bulletin of the Malaysian Mathematical Sciences Society. 2020 Jan;43:809-31.
10. Bejan CL, Sayar C. Generic Submanifolds of Almost Contact Metric Manifolds. Bulletin of the Malaysian Mathematical Sciences Society. 2022 Sep;45(5):2571-95.
11. Blair DE. A survey of Riemannian contact geometry. Complex Manifolds. 2019 Jan 1;6(1):31-64.
12. Akyol MA. Conformal generic submersions. Turkish Journal of Mathematics 45.1 (2021): 201-219.
13. Tanveer F, Akyol MA, Alzulaibani AA. "On a submersion of generic submanifold of a nearly Kaehler manifold." International Journal of Geometric Methods in Modern Physics 19.04 (2022): 2250048.
14. Akyol MA. Generic Riemannian Submersions from Almost Product Riemannian. Gazi University Journal of Science 30, no. 3 (2017): 89-100.