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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.06448 |
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| _version_ | 1866913193385787392 |
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| author | González-Dávila, J. C. |
| author_facet | González-Dávila, J. C. |
| contents | All invariant contact metric structures on tangent sphere bundles of each compact rank-one symmetric space are obtained explicitly, distinguishing for the orthogonal case those that are K-contact, Sasakian or 3-Sasakian. Only the tangent sphere bundle of complex projective spaces admits 3-Sasakian metrics and there exists a unique orthogonal Sasakian-Einstein metric. Furthermore, there is a unique invariant contact metric that is Einstein, in fact Sasakian-Einstein, on tangent sphere bundles of spheres and real projective spaces. Each invariant contact metric, Sasakian, Sasakian-Einstein or 3-Sasakian structure on the unit tangent sphere of any compact rank-one symmetric space is extended, respectively, to an invariant almost Kahler, Kahler, Kahler Ricci-flat or hyperKahler structure on the punctured tangent bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All invariant contact metric structures on tangent sphere bundles of compact rank-one symmetric spaces González-Dávila, J. C. Differential Geometry All invariant contact metric structures on tangent sphere bundles of each compact rank-one symmetric space are obtained explicitly, distinguishing for the orthogonal case those that are K-contact, Sasakian or 3-Sasakian. Only the tangent sphere bundle of complex projective spaces admits 3-Sasakian metrics and there exists a unique orthogonal Sasakian-Einstein metric. Furthermore, there is a unique invariant contact metric that is Einstein, in fact Sasakian-Einstein, on tangent sphere bundles of spheres and real projective spaces. Each invariant contact metric, Sasakian, Sasakian-Einstein or 3-Sasakian structure on the unit tangent sphere of any compact rank-one symmetric space is extended, respectively, to an invariant almost Kahler, Kahler, Kahler Ricci-flat or hyperKahler structure on the punctured tangent bundle. |
| title | All invariant contact metric structures on tangent sphere bundles of compact rank-one symmetric spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2401.06448 |