Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913507834855424 |
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| author | Sire, Yannick Xu, Tian |
| author_facet | Sire, Yannick Xu, Tian |
| contents | We introduce a new parabolic flow deforming any Riemannian metric on a spin manifold by following a constrained gradient flow of the total scalar curvature. This flow is built out of the well-known Dirac-Einstein functional. We prove local well-posedness of smooth solutions. The present contribution is the first installment of more general program on the Einstein-Dirac problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow Sire, Yannick Xu, Tian Analysis of PDEs Differential Geometry 53C27, 35R01 We introduce a new parabolic flow deforming any Riemannian metric on a spin manifold by following a constrained gradient flow of the total scalar curvature. This flow is built out of the well-known Dirac-Einstein functional. We prove local well-posedness of smooth solutions. The present contribution is the first installment of more general program on the Einstein-Dirac problem. |
| title | Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow |
| topic | Analysis of PDEs Differential Geometry 53C27, 35R01 |
| url | https://arxiv.org/abs/2409.12430 |