Immersions into Sasakian space forms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913405069164544 |
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| author | Loi, Andrea Placini, Giovanni Zedda, Michela |
| author_facet | Loi, Andrea Placini, Giovanni Zedda, Michela |
| contents | We study immersions of Sasakian manifolds into finite and infinite dimensional Sasakian space forms. After proving Calabi's rigidity results in the Sasakian setting, we characterise all homogeneous Sasakian manifolds which admit a (local) Sasakian immersion into a nonelliptic Sasakian space form. Moreover, we give a characterisation of homogeneous Sasakian manifolds which can be embedded into the standard sphere both in the compact and noncompact case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_05509 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Immersions into Sasakian space forms Loi, Andrea Placini, Giovanni Zedda, Michela Differential Geometry 53C25 (Primary) 53C30, 53C24, 53C42, 53A55 (Secondary) We study immersions of Sasakian manifolds into finite and infinite dimensional Sasakian space forms. After proving Calabi's rigidity results in the Sasakian setting, we characterise all homogeneous Sasakian manifolds which admit a (local) Sasakian immersion into a nonelliptic Sasakian space form. Moreover, we give a characterisation of homogeneous Sasakian manifolds which can be embedded into the standard sphere both in the compact and noncompact case. |
| title | Immersions into Sasakian space forms |
| topic | Differential Geometry 53C25 (Primary) 53C30, 53C24, 53C42, 53A55 (Secondary) |
| url | https://arxiv.org/abs/2305.05509 |