Classification of quaternionic skew-Hermitian symmetric spaces

Abstract

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