  We consider complete nearly K\"ahler manifolds with the canonical Hermitian
connection. We prove some metric properties of strict nearly K\"ahler manifolds
and give a sufficient condition for the reducibility of the canonical Hermitian
connection. A holonomic condition for a nearly K\"ahler manifold to be a
twistor space over a quaternionic K\"ahler manifold is given. This enables us
to give classification results in 10-dimensions.

Differential Geometry