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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.04421 |
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| _version_ | 1866929410494431232 |
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| author | Sykes, Daniel Schmalz, Gerd Ezhov, Vladimir |
| author_facet | Sykes, Daniel Schmalz, Gerd Ezhov, Vladimir |
| contents | In this article we consider spherical hypersurfaces in $\mathbb C^2$ with a fixed Reeb vector field as 3-dimensional Sasakian manifolds. We establish the correspondence between three different sets of parameters, namely, those arising from representing the Reeb vector field as an automorphism of the Heisenberg sphere, the parameters used in Stanton's description of rigid spheres, and the parameters arising from the rigid normal forms. We also geometrically describe the moduli space for rigid spheres, and provide geometric distinction between Stanton's hypersurfaces and those found by Ezhov and Schmalz. Finally, we determine the Sasakian automorphism groups of the rigid spheres and detect the homogeneous Sasakian manifolds among them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the classificarion of 3-dimensional spherical Sasakian manifolds Sykes, Daniel Schmalz, Gerd Ezhov, Vladimir Differential Geometry Complex Variables 32V05 In this article we consider spherical hypersurfaces in $\mathbb C^2$ with a fixed Reeb vector field as 3-dimensional Sasakian manifolds. We establish the correspondence between three different sets of parameters, namely, those arising from representing the Reeb vector field as an automorphism of the Heisenberg sphere, the parameters used in Stanton's description of rigid spheres, and the parameters arising from the rigid normal forms. We also geometrically describe the moduli space for rigid spheres, and provide geometric distinction between Stanton's hypersurfaces and those found by Ezhov and Schmalz. Finally, we determine the Sasakian automorphism groups of the rigid spheres and detect the homogeneous Sasakian manifolds among them. |
| title | On the classificarion of 3-dimensional spherical Sasakian manifolds |
| topic | Differential Geometry Complex Variables 32V05 |
| url | https://arxiv.org/abs/2407.04421 |