Slant submersions in paracontact geometry

Year 2020, , 822 - 834, 02.04.2020

Yılmaz Gündüzalp

https://doi.org/10.15672/hujms.458085

Cited By: 7

Abstract

In this paper, we investigate some geometric properties of three types of slant submersions whose total space is an almost paracontact metric manifold.

Keywords

almost paracontact metric manifold, semi-Riemannian submersion, proper slant submersion

References

• [1] M.A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys. 14 (7), 2017.
• [2] M.A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat. 46 (2), 177-192, 2017.
• [3] G. Baditoiu and S. Ianus, Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces, Diff. Geom. and appl. 16, 79-84, 2002.
• [4] J.P. Bourguignon and H.B. Lawson, A mathematician’s visit to Kaluza- Klein theory, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, 143-163, 1989.
• [5] J.P. Bourguignon and H.B. Lawson, Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79, 189-230, 1981.
• [6] A.V. Caldarella, On para-quaternionic submersions between para-quaternionic Kähler manifolds, Acta Applicandae Mathematicae 112, 1-14, 2010.
• [7] P. Dacko, On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (1), 193-213, 2004.
• [8] M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific, 2004.
• [9] Y. Gündüzalp and B. Sahin, Paracontact semi-Riemannian submersions, Turk. J.Math. 37 (1), 114-128, 2013.
• [10] Y. Gündüzalp, B. Sahin, Para-contact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. 37 (1), 139-152, 2014.
• [11] Y. Gündüzalp, Anti-invariant semi-Riemannian submersions from almost para- Hermitian manifolds, J. Funct. Spaces 2013, ID 720623, 2013.
• [12] Y. Gündüzalp, Slant submersions from almost product Riemannian manifolds, Turk. J. Math. 37, 863-873, 2013.
• [13] Y. Gündüzalp and M.A. Akyol, Conformal slant submersions from cosymplectic manifolds, Turk. J. Math. 42 (5), 2672-2689, 2018.
• [14] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715-737, 1967.
• [15] S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4, 1317-1352, 1987.
• [16] S. Ianus, and M. Visinescu, Space-time compactification and Riemannian submersions, The mathematical heritage of C.F. Gauss, World Sci. Publ., River Edge, NJ, 358-371, 1991.
• [17] S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104, 83-89, 2008.
• [18] S. Ianus, G.E. Vilcu and R.C. Voicu, Harmonic maps and Riemannian submersions between manifolds endowed with special structures, Banach Center Publications 93, 277-288, 2011.
• [19] I.K. Erken and C. Murathan, On slant Riemannian submersions for cosymplectic manifolds, Bull. Korean Math. Soc. 51 (6), 1749-1771, 2014.
• [20] B. O‘Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 459- 469, 1966.
• [21] B. O‘Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.
• [22] K.S.Park, H-slant submersions, Bull. Korean Math. Soc. 49, 329-338, 2012.
• [23] B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc.Sci. Math. Roumanie Tome. 54, 93-105, 2011.
• [24] B.Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J.Math 8 (3), 437-447, 2010.
• [25] H.M. Taştan, B.Sahin and Ş. Yanan , Hemi-slant submersions, Mediterr. J. Math. 13, 2171-2184, 2016.
• [26] J. Welyczko, On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results Math. 54, 377-387, 2009.
• [27] B. Watson, Almost Hermitian submersions, J. Differential Geom. 11, 147-165, 1976.
• [28] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geometry 36, 37-60, 2009.