A functional for Spin(7) forms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914948143120384 |
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| author | Lazaroiu, Calin Iuliu Shahbazi, C. S. |
| author_facet | Lazaroiu, Calin Iuliu Shahbazi, C. S. |
| contents | We characterize the set of all conformal Spin(7) forms on an oriented and spin Riemannian eight-manifold $(M,g)$ as solutions to a homogeneous algebraic equation of degree two for the self-dual four-forms of $(M,g)$. When $M$ is compact, we use this result to construct a functional whose self-dual critical set is precisely the set of all Spin(7) structures on $M$. Furthermore, the natural coupling of this potential to the Einstein-Hilbert action gives a functional whose self-dual critical points are conformally Ricci-flat Spin(7) structures. Our proof relies on the computation of the square of an irreducible and chiral real spinor as a section of a bundle of real algebraic varieties sitting inside the Kähler-Atiyah bundle of $(M,g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A functional for Spin(7) forms Lazaroiu, Calin Iuliu Shahbazi, C. S. Differential Geometry We characterize the set of all conformal Spin(7) forms on an oriented and spin Riemannian eight-manifold $(M,g)$ as solutions to a homogeneous algebraic equation of degree two for the self-dual four-forms of $(M,g)$. When $M$ is compact, we use this result to construct a functional whose self-dual critical set is precisely the set of all Spin(7) structures on $M$. Furthermore, the natural coupling of this potential to the Einstein-Hilbert action gives a functional whose self-dual critical points are conformally Ricci-flat Spin(7) structures. Our proof relies on the computation of the square of an irreducible and chiral real spinor as a section of a bundle of real algebraic varieties sitting inside the Kähler-Atiyah bundle of $(M,g)$. |
| title | A functional for Spin(7) forms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2409.08274 |