Classification of quaternionic skew-Hermitian symmetric spaces

Abstract

We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free ${\mathrm{SO}}^{\ast }(2n)\mathrm{Sp}(1)$-structure for arbitrary $n>1$. Moreover, we prove that any homogeneous quaternionic skew-Hermitian manifold is necessarily a symmetric space.

21 pages. Comments are welcome!