Non-singular weakly symmetric nilmanifolds
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913715057590272 |
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| author | Nikolayevsky, Y. Ziller, W. |
| author_facet | Nikolayevsky, Y. Ziller, W. |
| contents | A Riemannian manifold $M$ is called weakly symmetric if any two points in $M$ can be interchanged by an isometry. The compact ones have been well understood, and the main remaining case is that of 2-step nilpotent Lie groups. We give a complete classification of simply connected non-singular weakly symmetric nilmanifolds. Besides previously known examples, there are new families with 3-dimensional center, and a one-parameter family of dimensions 14. The classification is based on the authors classification of non-singular 2-step nilpotent Lie groups for which every geodesic is the image of a one parameter group of isometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-singular weakly symmetric nilmanifolds Nikolayevsky, Y. Ziller, W. Differential Geometry 53C30, 53C25, 22E25, 17B30 A Riemannian manifold $M$ is called weakly symmetric if any two points in $M$ can be interchanged by an isometry. The compact ones have been well understood, and the main remaining case is that of 2-step nilpotent Lie groups. We give a complete classification of simply connected non-singular weakly symmetric nilmanifolds. Besides previously known examples, there are new families with 3-dimensional center, and a one-parameter family of dimensions 14. The classification is based on the authors classification of non-singular 2-step nilpotent Lie groups for which every geodesic is the image of a one parameter group of isometries. |
| title | Non-singular weakly symmetric nilmanifolds |
| topic | Differential Geometry 53C30, 53C25, 22E25, 17B30 |
| url | https://arxiv.org/abs/2503.01170 |