Special solutions to the Type IIA flow
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866915082047324160 |
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| author | Raffero, Alberto |
| author_facet | Raffero, Alberto |
| contents | We consider the source-free Type IIA flow introduced by Fei-Phong-Picard-Zhang, and we study it in the case where the relevant geometric datum is a symplectic half-flat SU(3)-structure. We show the existence of ancient, immortal and eternal solutions to the flow, provided that the initial symplectic half-flat structure satisfies suitable properties. In particular, we prove that the solution starting at a symplectic half-flat structure with Hermitian Ricci tensor is ancient and evolves self-similarly by scaling the initial datum. These results apply to all known (locally) homogeneous spaces admitting invariant symplectic half-flat SU(3)-structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_12264 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Special solutions to the Type IIA flow Raffero, Alberto Differential Geometry High Energy Physics - Theory We consider the source-free Type IIA flow introduced by Fei-Phong-Picard-Zhang, and we study it in the case where the relevant geometric datum is a symplectic half-flat SU(3)-structure. We show the existence of ancient, immortal and eternal solutions to the flow, provided that the initial symplectic half-flat structure satisfies suitable properties. In particular, we prove that the solution starting at a symplectic half-flat structure with Hermitian Ricci tensor is ancient and evolves self-similarly by scaling the initial datum. These results apply to all known (locally) homogeneous spaces admitting invariant symplectic half-flat SU(3)-structures. |
| title | Special solutions to the Type IIA flow |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2107.12264 |