Canonical Submersions in Nearly Kähler Geometry

We explore submersions introduced by reducible holonomy representations of connections with parallel skew torsion. A submersion theorem extending previous, less general, results is given. As our main application we show that parallel 3-$(\alpha ,\delta )$-Sasaki manifolds admit 1-dimensional submersions onto nearly Kähler orbifolds. As a secondary application we reprove that a certain class of nearly Kähler manifolds submerges onto quaternionic Kähler manifolds. This new proof gives an direct expression for the quaternionic structure on the base.