Para-contact product semi-Riemannian submersions

Year 2017, Volume: 66 Issue: 2, 205 - 217, 01.08.2017

Yılmaz Gündüzalp

https://doi.org/10.1501/Commua1_0000000812

Abstract

We introduce the concept of para-contact product semi-Riemannian submersions from an almost para-contact metric manifold onto a semi-Riemannian product manifold. We provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost para-contact structure of the total manifold. Moreover, we investigate various properties of the O’Neill’s tensors of such submersions, fnd the integrability of the horizontal distribution. The paper is also focused on the transference of structures defined on the total manifold

Keywords

Almost para-contact metric manifold, semi-Riemannian product manifold, semi-Riemannian submersion, para-contact product semi-Riemannian submersion

References

• Akyol, M. A. and B. S.ahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1)(2016): 43-70.
• Akyol, M. A., Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics, (2016),Doi: 10.15672/HJMS.20174720336.
• Akyol, M. A., Conformal Semi-Invariant Submersions from Almost Product Riemannian Manifolds, Acta Math Vietnam (2016). doi:10.1007/s40306-016-0193-9
• Baditoiu, G. and S.Ianus, Semi-Riemannian submersions from real and complex pseudo- hyperbolic spaces, Diğ. Geom. and appl., 16(2002), 79-84.
• Caldarella, A.V., On para-quaternionic submersions between para-quaternionic Kähler man- ifolds, Acta Applicandae Mathematicae, 1(2010), 112, 1-14.
• Chinea, D., Almost contact metric submersions, Rend. Circ. Mat. Palermo, II Ser., 34(1985), 104.
• C. ayır, H., Some Notes on Lifts of Almost Paracontact Structures, American Review of Math- ematics and Statistics, 3(1), (2015): 52-60.
• Dacko, P. and Z. Olszak, On weakly para–cosymplectic manifolds of dimension 3, Journal of Geometry and Physics, 57(2007), 561-570.
• Falcitelli, M., S. Ianus, A. M. Pastore and M. Visinescu, Some applications of Riemannian submersions in physics, Rev. Roum. Phys., 48, (2003), 627-639.
• Falcitelli, M., S. Ianus, A.M. Pastore, Riemannian Submersions and Related Topics, World Scienti…c, 2004.
• Gündüzalp, Y. and B. S.ahin, Paracontact semi-Riemannian submersions, Turkish J.Math. (1), 114-128 (2013).
• Gündüzalp, Y. and B. S.ahin, 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. , (1967), 715-737.
• Ianus., S., R. Mazzocco, G.E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math., (2008), 104, 83-89.
• Ianus., S., S. Marchiafava, G.E. Vilcu, Paraquaternionic CR-submanifolds of para- quaternionic Kähler Manifols and semi-Riemannian submersions, Central European Journal of Mathematics, 4(2010), 8, 735-753.
• Kaneyuki, S., F.L. Williams, Almost para-contact and para-Hodge structures on manifolds, Nagoya Math. J. 99(1985), 173-187.
• Kılıc., E. and B. S.ahin, Radical anti-invariant lightlike submanifolds of semi-Riemannian product manifolds, Turkish J. Math., 32,(2008), 429-449.
• Mangione, V., Some submersions of CR-hypersurfaces of Kaehler-Einstein manifold, Inter- national Journal of Mathematics and Mathematical Sciences 2003(2003), 18:1137-1144.
• Montano, B.C., Bi-Legendrian structures and para-contact geometry, International Journal of Geometric Methods in Modern Physics, 3(2009), 6:487-504.
• O‘Neill, B., The fundamental equations of a submersion, Michigan Math. J., 13 (1966), 459–
• O‘Neill, B., Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.
• Senlin, X. and N. Yilong, Submanifolds of product Riemannian manifold, Acta Mathematica Scienta, 20B, (2000), 213-218.
• Watson, B., Almost Hermitian submersions, J. Diğ. Geom. 11, (1976), 147-165.
• Welyczko,J., On Legendre curves in 3-dimensional normal almost para-contact metric man- ifolds, Result.Math., 54(2009), 377-387.
• Yano, K. and M. Kon, Structures on manifolds. World Scienti…c Publishing Co., Singapore, Zamkovoy, S., Canonical connections on para-contact manifolds, Ann. Glob. Anal. Geom., (2009), 36,37-60.
• Current address : Department of Mathematics, Dicle University, 21280, Diyarbakır, Turkey.
• E-mail address : [e-mail]