Kähler manifold
Note that Sp("n") ⊂ SU(2"n") ⊂ U(2"n") ⊂ SO(4"n"), so every hyperkähler manifold is a Calabi–Yau manifold, every Calabi–Yau manifold is a Kähler manifold, and every Kähler manifold is orientable.