Curvature of quaternionic skew-Hermitian manifolds and bundle constructions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911830609231872 |
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| author | Chrysikos, Ioannis Cortés, Vicente Gregorovič, Jan |
| author_facet | Chrysikos, Ioannis Cortés, Vicente Gregorovič, Jan |
| contents | This articles is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Hermitian manifolds $(M, Q, ω)$. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic connections and we study qualitative properties of the induced Ricci tensor. Then we proceed with bundle constructions over such a manifold $(M, Q, ω)$. In particular, we prove the existence of almost hypercomplex skew-Hermitian structures on the Swann bundle over $M$ and investigate their integrability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature of quaternionic skew-Hermitian manifolds and bundle constructions Chrysikos, Ioannis Cortés, Vicente Gregorovič, Jan Differential Geometry 53C10, 53C26, 53D15 (Primary), 53C30, 53C35 (Secondary) This articles is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Hermitian manifolds $(M, Q, ω)$. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic connections and we study qualitative properties of the induced Ricci tensor. Then we proceed with bundle constructions over such a manifold $(M, Q, ω)$. In particular, we prove the existence of almost hypercomplex skew-Hermitian structures on the Swann bundle over $M$ and investigate their integrability. |
| title | Curvature of quaternionic skew-Hermitian manifolds and bundle constructions |
| topic | Differential Geometry 53C10, 53C26, 53D15 (Primary), 53C30, 53C35 (Secondary) |
| url | https://arxiv.org/abs/2404.05463 |