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Pointwise slant submersions from cosymplectic manifolds

In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples. | Turk J Math (2016) 40: 582 – 593 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ doi:10.3906/mat-1503-98 Research Article Pointwise slant submersions from cosymplectic manifolds ¨ 2,∗ Sezin AYKURT SEPET1 , Mahmut ERGUT Department of Mathematics, Arts and Science Faculty, Ahi Evran University, Kır¸sehir, Turkey 2 Department of Mathematics, Arts and Science Faculty, Namık Kemal University, Tekirda˘ g, Turkey 1 Received: 31.03.2015 • Accepted/Published Online: 09.09.2015 • Final Version: 08.04.2016 Abstract: In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples. Key words: Riemannian submersion, almost contact metric manifold, cosymplectic manifold, pointwise slant submersion 1. Introduction An important topic in differential geometry is the Riemannian submersions between Riemannian manifolds introduced by O’Neill [12] and Gray [5]. Such submersions were generalized by Watson to almost Hermitian manifolds by proving that the base manifold and each fiber have the same kind of structure as the total space in most cases [21]. Recently, many works considering different conditions on Riemannian submersion have been done (see [3, 4, 6, 7, 8, 13, 15, 17, 19, 20]). Sahin [18] introduced slant submersions from almost Hermitian manifolds onto Riemannian manifolds in such a way that let π be a Riemannian submersion from an almost Hermitian manifold (M1 , g1 , J1 ) onto a Riemannian manifold (M2 , g2 ) . If for any nonzero vector X ∈ Γ (ker π∗ ), the angle θ(X) between JX and the space ker π∗ is a constant, i.e. it is independent of the choice of the point p ∈ M1 and choice of the tangent vector X in ker π∗ , then we say that π is a slant submersion. In this case, the angle θ is called the slant angle of the slant submersion. He gave some examples and investigated the geometry of leaves of the distributions for such submersions. Furthermore, Lee .