On Quasi-Hemi-Slant Riemannian Maps

Abstract

In this paper, quasi-hemi-slant Riemannian maps from almost Hermitian manifolds onto Riemannian manifolds are introduced. The geometry of leaves of distributions that are involved in the definition of the submersion and quasi-hemi-slant Riemannian maps are studied. In addition, conditions for such distributions to be integrable and totally geodesic are obtained. Also, a necessary and sufficient condition for proper quasi-hemi-slant Riemannian maps to be totally geodesic is given. Moreover, structured concrete examples for this notion are given.

Keywords

• Riemannian maps
• Semi-invariant maps
• Quasi bi-slant maps
• Quasi hemi-slant

References

1. [1] Sahin, B., “Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications”, Elsevier: Academic Press (2017).
2. [2] Lerner, D.E., Sommers, P.D., “Complex Manifold Techniques in Theoretical Physics”, Research Notes in Mathematics; 32, Pitman Advanced Publishing, (1979).
3. [3] Chandelas, P., Horowitz, G.T., Strominger, A., Witten, E., “Vacuum configurations for super-strings”, Nuclear Physics B, 258: 46-74, (1985).
4. [4] Tromba, A.J. “Teichmuller Theory in Riemannian Geometry”, Lectures in Mathematics: ETH Zurich, Birkhauser, Basel, (1992).
5. [5] Esposito, G., “From spinor geometry to complex general relativity”, International Journal of Geometric Methods in Modern Physics., 2: 675–731, (2005).
6. [6] O’Neill’s B., “The fundamental equations of a submersion”, The Michigan Mathematical Journal, 33(13): 459–469, (1966).
7. [7] Gray, A., “Pseudo-Riemannian almost product manifolds and submersions”, Journal of Mathematics and Mechanics, 16: 715-738, (1967).
8. [8] Watson, B., “Almost Hermitian submersions”, Journal of Differential Geometry, 11(1): 147-165, (1976).

9. [9] Falcitelli, M., Ianus, S., Pastore, A.M., “Riemannian Submersions and Related Topics”. World Scientific: River Edge, NJ, (2004).
10. [10] Chinea, D., “Almost contact metric submersions”, Rendiconti del Circolo Matematico del Palermo, 34(1): 89–104, (1985).
11. [11] Park, K.S., Prasad, R., “Semi-slant submersions”, Bulletin of the Korean Mathematical Society., 50: 951- 962, (2013).
12. [12] Sahin, B.,” Generic Riemannian maps”, Miskolc Mathematical Notes 18(1): 453–467, (2017).
13. [13] Akyol, M.A., Sari, R., Aksoy, E., “Semi-invariant ξ⊥ Riemannian submersions from almost Contact metric manifolds”, International Journal of Geometric Methods in Modern Physics, 14(5): 1750075, (2017).
14. [14] Tastan, H.M., Sahin, B., Yanan, S., “Hemi-slant submersions”, Mediterranean Journal of Mathematics., 13(4): 2171-2184, (2016).
15. [15] Sayar, C., Akyol, M.A., Prasad, R., “Bi-slant submersions in complex geometry”, International Journal of Geometric Methods in Modern Physics, 17(4): 2050055-44, (2020).
16. [16] Prasad, R., Shukls, S. S., Kumar, S., “On Quasi-bi-slant Submersions”, Mediterranean Journal of Mathematics 16(6): December, (2019).
17. [17] Longwap, S., Massamba, F., Homti, N.E., “On Quasi-Hemi-Slant Riemannian Submersion” Journal of Advances in Mathematics and Computer Science, 34(1): 1–14, (2019).
18. [18] Fischer, A.E., “Riemannian maps between Riemannian manifolds”, Contemporary Mathematics., 132: 331–366, (1992).
19. [19] Blair, D. E., “Riemannian geometry of contact and symplectic manifolds”, Progress in Mathematics:203, Birkhauser Boston, Basel, Berlin, (2002).
20. [20] De, U.C., Sheikh, A.A., “Complex manifolds and Contact manifolds”, Narosa publishing: January, (2009).
21. [21] Baird, P., Wood, J.C., “Harmonic Morphism between Riemannian Manifolds”, Oxford science publications: Oxford. (2003).