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Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds

he purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. | Turk J Math (2016) 40: 540 – 552 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ doi:10.3906/mat-1504-47 Research Article Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds ˙ Irem ˙ ¨ Ay¸se BERI, KUPEL I˙ ERKEN∗, Cengizhan MURATHAN Department of Mathematics, Faculty of Arts and Science, Uluda˘ g University, Bursa, Turkey Received: 16.04.2015 • Accepted/Published Online: 04.09.2015 • Final Version: 08.04.2016 Abstract: The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved the nonexistence of (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that the characteristic vector field ξ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field ξ is a horizontal vector field and an anti-invariant horizontally conformal submersion such that ξ is a vertical vector field. Key words: Riemannian submersion, conformal submersion,Warped product, Kenmotsu manifold, Anti-invariant Riemannian submersion 1. Introduction Riemannian submersions between Riemannian manifolds were studied by O’Neill [16] and Gray [9]. Riemannian submersions have several applications in mathematical physics. Indeed, Riemannian submersions have their applications in the Yang–Mills theory [4, 27], Kaluza–Klein theory [5, 10], supergravity and superstring theories [11, 28], etc. Later such submersions were considered between manifolds with differentiable structures; see [8]. Furthermore, we have the following submersions: semi-Riemannian .