Classification of quaternionic skew-Hermitian symmetric spaces

Ioannis Chrysikos; Jan Gregorovič

Classification of quaternionic skew-Hermitian symmetric spaces

Differential Geometry 2026-01-21 v1 Symplectic Geometry

Authors: Ioannis Chrysikos , Jan Gregorovič

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.

Keywords

quaternionic skew-Hermitian symmetric spaces torsion-free structure homogeneous manifold symmetric spaces SO*(2n)Sp(1)-structure

Cite

@article{arxiv.2601.13036,
  title  = {Classification of quaternionic skew-Hermitian symmetric spaces},
  author = {Ioannis Chrysikos and Jan Gregorovič},
  journal= {arXiv preprint arXiv:2601.13036},
  year   = {2026}
}

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21 pages. Comments are welcome!

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