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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.27585 |
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| _version_ | 1866914606590459904 |
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| author | Cidre-Díaz, Ángel Olmos, Carlos E. Rodríguez-Vázquez, Alberto |
| author_facet | Cidre-Díaz, Ángel Olmos, Carlos E. Rodríguez-Vázquez, Alberto |
| contents | We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric space, and of every homogeneous $S^1$-bundle over a compact irreducible symmetric space. Moreover, we construct irreducible homogeneous metrics whose leaves of symmetry are symmetric spaces of arbitrarily large rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27585 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The index of symmetry and homogeneous fibrations Cidre-Díaz, Ángel Olmos, Carlos E. Rodríguez-Vázquez, Alberto Differential Geometry 53C30, 53C35 We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric space, and of every homogeneous $S^1$-bundle over a compact irreducible symmetric space. Moreover, we construct irreducible homogeneous metrics whose leaves of symmetry are symmetric spaces of arbitrarily large rank. |
| title | The index of symmetry and homogeneous fibrations |
| topic | Differential Geometry 53C30, 53C35 |
| url | https://arxiv.org/abs/2605.27585 |