Semi-invariant semi-Riemannian submersions

Year 2018, Volume: 67 Issue: 1, 80 - 92, 01.02.2018

Mehmet Akif Akyol Yılmaz Gündüzalp

https://doi.org/10.1501/Commua1_0000000832

Cited By: 5

Abstract

In this paper, we introduce semi-invariant semi-Riemannian submersions from para-Kähler manifolds onto semi-Riemannian manifolds. Wegive some examples, investigate the geometry of foliations that arise fromthe de…nition of a semi-Riemannian submersion and check the harmonicity ofsuch submersions. We also find necessary and su¢ cient conditions for a semiinvariant semi-Riemannian submersion to be totally geodesic. Moreover, weobtain curvature relations between the base manifold and the total manifold

Keywords

Para-Kähler manifold, semi-Riemannian submersion, anti-invariantsemi-Riemannian submersion, semi-invariant semi-Riemannian submersion

References

• Akyol, M. A., Sarı, R. and Aksoy, E.: Semi-invariant ? Riemannian submersions from almost contact metric manifolds,Int. J. Geom. Methods Mod. Phys., 1142/S0219887817500748, (2017). DOI: Baditoiu, G., Ianus, S.
• Semi-Riemannian submersions from real and complex pseudo- hyperbolic spaces. Diğ. Geom. and appl. 16, 79-84 (2002).
• Bejancu, A.: Geometry of CR-submanifolds. Mathematics and its Applications(East Euro- pean Series), 23, D. Reidel Publishhing Co., Dordrecht, 1986.
• Caldarella, A.V.: On para-quaternionic submersions between para-quaternionic Kähler man- ifolds. Acta Applicandae Mathematicae 112, 1-14 (2010)
• Chinea, D.: Almost contact metric submersions. Rend. Circ. Mat. Palermo, II Ser. 34, 89-104 (1985).
• Çayır, H. Akdaµg, K.: Some notes on almost para-complex structures associated with the diagonal lifts and operators on cotangent bundle T (Mn). New Trends in Mathematical Sciences. 4 (4), 42-50 (2016).
• Etayo, F., Fioravanti, M. and Trias, U.R.: On the submanifolds of an almost para-hermitian manifold. Acta math. Hungar 85(4), 277-286 (1999).
• Falcitelli, M., Ianus, S. and Pastore, A.M.: Riemannian Submersions and Related Topics. World Scienti…c, 2004.
• Falcitelli, M., Ianus, S., Pastore, A.M. and Visinescu, M.: Some applications of Riemannian submersions in physics. Rev. Roum. Phys. 48, 627-639 (2003).
• Gündüzalp, Y. and S.ahin, B.: Paracontact semi-Riemannian submersions. Turkish J.Math. (1), 114-128 (2013).
• Gündüzalp, Y.: Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds. Journal of Function Spaces and Applications,ID 720623,(2013).
• Gündüzalp, Y. and S.ahin, B.: Para-contact para-complex semi-Riemannian submersions. Bull. Malays. Math. Sci. Soc. 37(1), 139-152 (2014).
• Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. , 715-737 (1967)
• Ianus, S., Mazzocco, R. and Vilcu, G.E.: Riemannian submersions from quaternionic mani- folds. Acta Appl. Math. 104, 83-89 (2008).
• Ianus, S., Marchiafava, S. and Vilcu, G.E.: Para-quaternionic CR-submanifolds of para- quaternionic Kähler Manifols and semi-Riemannian submersions. Central European Journal of Mathematics 4,735-753 (2010).
• Ianus, S., Vilcu, G.V. and Voicu, R.C:: Harmonic maps and Riemannian submersions between manifolds endowed with special structures. Banach Center Publications 93 , 277-288 (2011).
• Ivanov, S. and Zamkovoy, S.: Para-Hermitian and para-quaternionic manifolds. Diğ. Geom. and Its Appl. 23, 205-234 (2005).
• Libermann, P.: Sur les structures presque para-complexes. C.R. Acad. Sci. Paris Ser. I Math. , 2517-2519 (1952)
• O‘Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13, 459– 469 (1966).
• O‘Neill, B.: Semi-Riemannian Geometry with Application to Relativity. Academic Press, New York, 1983.
• Park, K.S.: H-semi-invariant submersions. Taiwanese Journal of Math. 16(5), 1865-1878 (2012).
• S.ahin, B.: Semi-invariant Riemannian submersions from almost Hermitian manifolds. Cana- dian Mathematical Bulletin, Doi:10.4153/CMB-2011-144-8.
• S.ahin, B.: Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math. (2) (2013), 629-659.
• S.ahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications, Elsevier, Academic Press, (2017).
• Rashevskij, P.K.: The scalar …eld in a strati…ed space. Trudy Sem. Vektor. Renzor. Anal. 6, 248 (1948).
• Watson, B.: Almost Hermitian submersions. J. Diğerential Geom. 11, 147-165 (1976).
• Current address : Mehmet Akif Akyol: Department of Mathematics, Bingöl University 12000, Bingöl TURKEY