Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917568290226176 |
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| author | Hofmann, Jordan |
| author_facet | Hofmann, Jordan |
| contents | We give a spinorial construction of Sasakian and 3-Sasakian structures in arbitrary dimension, generalizing previously known results in dimensions 5 and 7. Furthermore, we obtain a complete description of the space of invariant spinors on a homogeneous 3-Sasakian space, and show that it is spanned by the Clifford products of invariant differential forms with a certain invariant Killing spinor. Finally, we give a basis for the space of invariant Riemannian Killing spinors on a homogeneous 3-Sasakian space, and determine which of these induce the homogeneous 3-Sasakian structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09301 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint Hofmann, Jordan Differential Geometry 22E46, 22F30, 53C25, 53C27, 53C30 We give a spinorial construction of Sasakian and 3-Sasakian structures in arbitrary dimension, generalizing previously known results in dimensions 5 and 7. Furthermore, we obtain a complete description of the space of invariant spinors on a homogeneous 3-Sasakian space, and show that it is spanned by the Clifford products of invariant differential forms with a certain invariant Killing spinor. Finally, we give a basis for the space of invariant Riemannian Killing spinors on a homogeneous 3-Sasakian space, and determine which of these induce the homogeneous 3-Sasakian structure. |
| title | Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint |
| topic | Differential Geometry 22E46, 22F30, 53C25, 53C27, 53C30 |
| url | https://arxiv.org/abs/2208.09301 |