Classification of quaternionic skew-Hermitian symmetric spaces

TL;DR

This paper classifies all quaternionic skew-Hermitian symmetric spaces and proves that any homogeneous quaternionic skew-Hermitian manifold must be symmetric, advancing understanding of their geometric structure.

Contribution

It provides a complete classification of quaternionic skew-Hermitian symmetric spaces and establishes that all homogeneous such manifolds are symmetric spaces.

Findings

Complete classification of quaternionic skew-Hermitian symmetric spaces

Proof that all homogeneous quaternionic skew-Hermitian manifolds are symmetric

Identification of torsion-free ${ m SO}^{*}(2n){ m Sp}(1)$-structures

Abstract

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