Anti-invariant \({\xi^{\bot}}\)-Riemannian submersions from hyperbolic \(\beta\)-Kenmotsu manifolds
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Mohd Danish Siddiqi
anallintegral@gmail.com
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Mehmet Akif Akyol
mehmetakifakyol@bingol.edu.tr
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DOI:
https://doi.org/10.4067/S0719-06462018000100079Abstract
In this paper, we introduce anti-invariant \({\xi^{\bot}}\)-Riemannian submersions from Hyperbolic β-Kenmotsu Manifolds onto Riemannian manifolds. Necessary and sufficient conditions for a special anti-invariant \({\xi^{\bot}}\)-Riemannian submersion to be totally geodesic are studied. Moreover, we obtain decomposition theorems for the total manifold of such submersions.
Keywords
[1] Chinea, C. Almost contact metric submersions, Rend. Circ. Mat. Palermo, 43(1), 89-104, 1985.
[2] Eells, J., Sampson, J. H. Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86, 109-160. 1964.
[3] Falcitelli, M., Ianus, S., Pastore, A. M. Riemannian submersions and Related topics, (World Scientific, River Edge, NJ, 2004.
[4] Gray, A. Pseudo-Riemannian almost product manifolds and submersion, J. Math. Mech., 16, 715-737, 1967.
[5] Ianus, S., Pastore, A. M., Harmonic maps on contact metric manifolds, Ann. Math. Blaise Pascal, 2(2), 43-53, 1995.
[6] Lee, J. W., Anti-invariant ξ⊥− Riemannian submersions from almost contact manifolds, Hacettepe J. Math. Stat. 42(2), 231-241, 2013.
[7] O‘Neill , B. The fundamental equations of a submersions, Mich. Math. J., 13, 458-469, 1996.
[8] Sahin, B. Anti-invariant Riemannian submersions from almost hermition manifolds, Cent. Eur. J. Math., 8(3), 437-447, 2010.
[9] Siddiqi, M. D., Ahmed, M and Ojha, J.P., CR-submanifolds of nearly-trans hyperbolic sasakian manifolds admitting semi-symmetric non-metric connection, Afr. Diaspora J. Math. (N.S.), Vol 17(1), 93-105, 2014.
[10] Upadhyay, M. D, Dube., K. K., Almost contact hyperbolic (f, g, η, ξ) structure, Acta. Math. Acad. Scient. Hung., Tomus, 28, 1-4, 1976.
[11] Watson, B. Almost Hermitian submersions, J. Differential Geometry, 11(1), 147-165, 1976.
[2] Eells, J., Sampson, J. H. Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86, 109-160. 1964.
[3] Falcitelli, M., Ianus, S., Pastore, A. M. Riemannian submersions and Related topics, (World Scientific, River Edge, NJ, 2004.
[4] Gray, A. Pseudo-Riemannian almost product manifolds and submersion, J. Math. Mech., 16, 715-737, 1967.
[5] Ianus, S., Pastore, A. M., Harmonic maps on contact metric manifolds, Ann. Math. Blaise Pascal, 2(2), 43-53, 1995.
[6] Lee, J. W., Anti-invariant ξ⊥− Riemannian submersions from almost contact manifolds, Hacettepe J. Math. Stat. 42(2), 231-241, 2013.
[7] O‘Neill , B. The fundamental equations of a submersions, Mich. Math. J., 13, 458-469, 1996.
[8] Sahin, B. Anti-invariant Riemannian submersions from almost hermition manifolds, Cent. Eur. J. Math., 8(3), 437-447, 2010.
[9] Siddiqi, M. D., Ahmed, M and Ojha, J.P., CR-submanifolds of nearly-trans hyperbolic sasakian manifolds admitting semi-symmetric non-metric connection, Afr. Diaspora J. Math. (N.S.), Vol 17(1), 93-105, 2014.
[10] Upadhyay, M. D, Dube., K. K., Almost contact hyperbolic (f, g, η, ξ) structure, Acta. Math. Acad. Scient. Hung., Tomus, 28, 1-4, 1976.
[11] Watson, B. Almost Hermitian submersions, J. Differential Geometry, 11(1), 147-165, 1976.
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Published
2018-10-19
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[1]
M. Danish Siddiqi and M. Akif Akyol, “Anti-invariant \({\xi^{\bot}}\)-Riemannian submersions from hyperbolic \(\beta\)-Kenmotsu manifolds”, CUBO, vol. 20, no. 1, pp. 79–94, Oct. 2018.
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