Complex quaternionic manifolds and c-projective structures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912795750039552 |
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| author | Borówka, Aleksandra |
| author_facet | Borówka, Aleksandra |
| contents | We discuss complex quaternionic manifolds, i.e., those that have holonomy $GL(n,\mathbb{H})U(1)$, which naturally arise via quaternionic Feix--Kaledin construction. We show that for a fixed c-projective class, any real analytic connection with type $(1,1)$ curvature induces, via quaternionic Feix--Kaledin construction, an $S^1$-invariant connection with holonomy contained in $GL(n,\mathbb{H})U(1)$. As an application, we characterize in this setting the distinguished $U^*(2n):=SL(n,\mathbb{H})U(1)$ connection studied in Battaglia \cite{Bat} and Hitchin \cite{Hit3}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex quaternionic manifolds and c-projective structures Borówka, Aleksandra Differential Geometry 53C26, 53C28 We discuss complex quaternionic manifolds, i.e., those that have holonomy $GL(n,\mathbb{H})U(1)$, which naturally arise via quaternionic Feix--Kaledin construction. We show that for a fixed c-projective class, any real analytic connection with type $(1,1)$ curvature induces, via quaternionic Feix--Kaledin construction, an $S^1$-invariant connection with holonomy contained in $GL(n,\mathbb{H})U(1)$. As an application, we characterize in this setting the distinguished $U^*(2n):=SL(n,\mathbb{H})U(1)$ connection studied in Battaglia \cite{Bat} and Hitchin \cite{Hit3}. |
| title | Complex quaternionic manifolds and c-projective structures |
| topic | Differential Geometry 53C26, 53C28 |
| url | https://arxiv.org/abs/2412.10301 |