Pointwise Bi-Slant Submersions

In the present paper we study pointwise bi-slant submersions from almost Hermitian manifolds ontoRiemannian manifolds as a generalization of anti-invariant, semi-invariant, slant, bi-slant, pointwise semislant, pointwise slant, pointwise hemi-slant submersions. We mainly focus on pointwise bi-slantsubmersions from Kaehler manifolds onto Riemannian manifolds. We give some characterizations forsuch maps. We obtain necessary and sufficient conditions for the totally geodesicness of the distributions?1 and ?2 mentioned in the definition of the pointwise bi-slant submersions. Also we investigate thegeometry of vertical and horizontal distributions. Then we give necessary and sufficient conditions forpointwise bi-slant submersions to be totally geodesic.

PDF

___

1. Akyol, MA, Sahin, B. 2016. Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics.; 40: 43-70.
2. Akyol, MA, Gündüzalp, Y. 2016. Hemi-slant submersions from almost product Riemannian manifolds. Gulf Journal of Mathematics; 4(3): 15-27.
3. Alqahtani, LS, Stankovic, MS, Uddin, S. 2017. Warped Product Bislant Submanifolds of Cosymplectic Manifolds. Filomat; 31(16): 5065-5071.
4. Aykurt Sepet, S, Ergüt, M. 2016. Pointwise slant submersions from cosymplectic manifolds. Turkish Journal of Mathematics; 40: 582- 593.
5. Baird, P, Wood, JC. Harmonic morphisms between Riemannian manifolds. London Mathematical Society Monographs, Oxford University Press, Oxford 2003.
6. Cabrerizo, JL, Carriazo, A, Fernandez, LM, Fernandez, M. 1999. Slant Submanifolds in Sasakian Manifolds. Geometriae Dedicata; 183-199.
7. Carriazo, A. “Bi-slant Immersions,” In Proceeding of the ICRAMS, 2000, 88-97.
8. Falcitelly, M, Ianus, S, Pastore, AM. Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
9. Gray, A. 1967. Pseudo-Riemannian almost product manifolds and submersions. Journal of Mathematics and Mechanics.; 16: 715-737.
10. Gündüzalp, Y. 2013. Slant submersions from almost product Riemannian manifolds. Turkish Journal of Mathematics.; 37: 863-873.
11. Gündüzalp, Y. 2016. Semi-slant submersions from almost product Riemannian manifolds. Demonstratio Mathematica; 49(3): 345-356.
12. Lee, JW, Sahin, B. 2014. Pointwise slant submersions. Bulletin of the Korean Mathematical Society; 51(4): 1115-1126.
13. O’Neill, B. 1966. The fundamental equations of a submersion. Michigan Mathematical Journal.; 13: 458-469.
14. Park, KS, Prasad, R. 2013. Semi-slant submersions. Bulletin of the Korean Mathematical Society; 50(3): 951-962.
15. Şahin, B. 2010. Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European Journal of Mathematics; 8(3): 437-447.
16. Şahin, B. 2011. Semi-invariant Riemannian submersions from almost Hermitian manifolds. Canadian Mathematical Bulletin; 56: 173-183.
17. Şahin, B. 2011. Slant submersions from almost Hermitian manifolds. Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie; 54(102): 93-105.
18. Sayar, C, Taştan, HM, Özdemir, F, Tripathi, MM. 2020. Generic submersions from Kaehlerian Manifolds. Bulletin of the Malaysian Mathematical Sciences Society; 43: 809-831.
19. Taştan HM, Şahin B, Yanan, Ş. 2016. Hemi-slant submersions. Mediterranean Journal of Mathematics; 13: 2171-2184.
20. Tastan, HM. 2017. Lagrangian submersions from normal almost contact manifolds. Filomat; 31(12): 3885-3895.
21. Uddin, S, Chen, BY, Al-Solamy, FR. 2017. Warped Product Bislant Immersions in Kaehler Manifolds. Mediterranean Journal of Mathematics; 14 (95).
22. Watson, B. Almost Hermitian submersions. 1976. Journal of Differential Geometry; 11(1): 147-165.