Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds

Abstract

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 that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that 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.

On Conformal Anti-Invariant Submersions Whose Total Manifolds Are Locally Product Riemannian

“…where V and H are the vertical and horizontal projections (see [25]). On the other hand, from (5) and (6), we have…”

“…In this case, the fibers are anti-invariant with respect to the almost complex structure of the total manifold. This notion extended to different total spaces see: [5][6][7][8][9][10][11][12][13][14].…”

Isotropic Riemannian submersions

“…Recently, B. Şahin [27] introduced the notion of anti-invariant Riemannian submersions which are Riemannian submersions from almost Hermitian manifolds such that the vertical distribution is anti-invariant under the almost complex structure of the total manifold. Later this notion has been extended for several cases, see: [1,2,4,8,9,16,19,20,23,26,29,30,32].…”

Anti-invariant Riemanian submersions from nearly-k-cosymplectic manifolds

“…Recently, C. Murathan and I. Küpeli Erken have investigated anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds and from cosymplectic manifolds onto Riemannian manifolds ( [11,12]). Furthermore, anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds have also been studied in [2].…”