Submanifolds of almost quaternionic skew-Hermitian manifolds

Abstract

We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds $(M^{4n}, Q, \omega)$, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the torsion-free case, we realize each type of submanifold considered in the theoretical part by constructing explicit examples of submanifolds of semisimple quaternionic skew-Hermitian symmetric spaces.