Two well-known slogans are
A Sasakian manifold is the odd dimensional analogue of a Kähler manifold
A $3$-Sasakian manifold is the odd dimensional analogue of a hyper-Kähler manifold
Does this analogy extend to quaternion-Kähler manifolds? Is there a notion of quaternion-Sasakian manifolds?
What about special holonomy? Does there exist a notion of $Spin(7)$-Sasakian manifold. What about $G_2$-holonomy?
Can one use find an even dimensional analogue?