Classification of quaternionic skew-Hermitian symmetric spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912832200638464 |
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| author | Chrysikos, Ioannis Gregorovič, Jan |
| author_facet | Chrysikos, Ioannis Gregorovič, Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of quaternionic skew-Hermitian symmetric spaces Chrysikos, Ioannis Gregorovič, Jan Differential Geometry Symplectic Geometry 53C10, 53C15, 53C30, 53C35 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. |
| title | Classification of quaternionic skew-Hermitian symmetric spaces |
| topic | Differential Geometry Symplectic Geometry 53C10, 53C15, 53C30, 53C35 |
| url | https://arxiv.org/abs/2601.13036 |