Conformal slant submersions from cosymplectic manifolds

Abstract

Akyol [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant submersions from cosymplectic manifolds.The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field ξ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, and conformal antiinvariant submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, the geometry of foliations, some conditions related to total geodesicness, and harmonicity of the submersions. Finally, we consider a decomposition theorem on the total space of the new submersion.

On generalized weakly symmetric $\alpha$-cosymplectic manifolds

“…where ∇ denotes the Riemannian connection holds and α is a real number, then (M 2n+1 , φ, ξ, η, g) is called an α-cosymplectic manifold ( [1,2,10,13,15]). In this case, it is well known that…”

Conformal bi-slant submersions

“…Recently, Akyol and Şahin have introduced conformal anti-invariant submersions [2], conformal semiinvariant submersion [3], conformal slant submersion [5], and conformal semi-slant submersions [1]. Also, the geometry of conformal submersions have been studied by several authors [18,22].…”

Slant submersions in paracontact geometry

“…Given a C ∞ −submersion ψ from a (semi)-Riemannian manifold (N, g N ) onto a (semi)-Riemannian manifold (B, g B ), according to the circumstances on the map ψ : (N, g N ) → (B, g B ), we get the following: a (semi)-Riemannian submersion ( [3,8,14,20]), an almost Hermitian submersion ( [27]), a paracontact submersion ( [9]), a paracontact paracomplex submersion ( [10]), a (para) quaternionic submersion ( [6,17]), a slant submersion ( [12,19,22,23]), an anti-invariant submersion ( [11,24]), a conformal semi-slant submersion ( [1,13]), a conformal anti-invariant submersion ( [2]), a hemi-slant submersion ( [25]), etc. As we know, Riemannian submersions were severally introduced by B. O'Neill ( [20]) and A.…”