Variation formulae for the volume of coassociative submanifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909446948519936 |
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| author | Pacini, Tommaso Raffero, Alberto |
| author_facet | Pacini, Tommaso Raffero, Alberto |
| contents | We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of $G_2$ data. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds; this formula highlights the role of the ambient torsion and Ricci curvature. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13956 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Variation formulae for the volume of coassociative submanifolds Pacini, Tommaso Raffero, Alberto Differential Geometry We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of $G_2$ data. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds; this formula highlights the role of the ambient torsion and Ricci curvature. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non. |
| title | Variation formulae for the volume of coassociative submanifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2207.13956 |