Deformation theory of nearly $\mathrm{G}_2$ manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866916184281055232 |
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| author | Dwivedi, Shubham Singhal, Ragini |
| author_facet | Dwivedi, Shubham Singhal, Ragini |
| contents | We study the deformation theory of nearly $\mathrm{G}_2$ manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\mathrm{G}_2$ structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly $\mathrm{G}_2$ structure on the Aloff--Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly $\mathrm{G}_2$ manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_02497 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Deformation theory of nearly $\mathrm{G}_2$ manifolds Dwivedi, Shubham Singhal, Ragini Differential Geometry 53C15, 53C25, 53C29 We study the deformation theory of nearly $\mathrm{G}_2$ manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\mathrm{G}_2$ structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly $\mathrm{G}_2$ structure on the Aloff--Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly $\mathrm{G}_2$ manifolds. |
| title | Deformation theory of nearly $\mathrm{G}_2$ manifolds |
| topic | Differential Geometry 53C15, 53C25, 53C29 |
| url | https://arxiv.org/abs/2007.02497 |