Subspaces of a para-quaternionic Hermitian vector space

Abstract

Let $(\tilde{Q},g)$ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V,\tilde{Q},g)\simeq (H^2\otimes E^{2n},\mathfrak{sl}(H),{\omega }^H\otimes {\omega }^E)$, we give an explicit description, from an affine and metric point of view, of main classes of subspaces of $V$ which are invariantly defined with respect to the structure group of $\tilde{Q}$ and $(\tilde{Q},g)$ respectively.