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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.12225 |
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| _version_ | 1866915113646161920 |
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| author | Cortés, Vicente Gil-García, Alejandro Röser, Markus |
| author_facet | Cortés, Vicente Gil-García, Alejandro Röser, Markus |
| contents | This paper is concerned with the geometry of principal orbits in quaternionic Kähler manifolds $M$ of cohomogeneity one. We focus on the complete cohomogeneity one examples obtained from the non-compact quaternionic Kähler symmetric spaces associated with the simple Lie groups of type A by the one-loop deformation. We prove that for zero deformation parameter the principal orbits form a fibration by solvsolitons (nilsolitons if $4n=\dim M=4$). The underlying solvable group is non-unimodular if $n>1$ and is the Heisenberg group if $n=1$. We show that under the deformation, the hypersurfaces remain solvmanifolds but cease to be Ricci solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternionic Kähler manifolds fibered by solvsolitons Cortés, Vicente Gil-García, Alejandro Röser, Markus Differential Geometry 53C25, 53C26, 53C40 This paper is concerned with the geometry of principal orbits in quaternionic Kähler manifolds $M$ of cohomogeneity one. We focus on the complete cohomogeneity one examples obtained from the non-compact quaternionic Kähler symmetric spaces associated with the simple Lie groups of type A by the one-loop deformation. We prove that for zero deformation parameter the principal orbits form a fibration by solvsolitons (nilsolitons if $4n=\dim M=4$). The underlying solvable group is non-unimodular if $n>1$ and is the Heisenberg group if $n=1$. We show that under the deformation, the hypersurfaces remain solvmanifolds but cease to be Ricci solitons. |
| title | Quaternionic Kähler manifolds fibered by solvsolitons |
| topic | Differential Geometry 53C25, 53C26, 53C40 |
| url | https://arxiv.org/abs/2501.12225 |