Initial value problems on cohomogeneity one manifolds, I
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915054639644672 |
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| author | Verdiani, Luigi Ziller, Wolfgang |
| author_facet | Verdiani, Luigi Ziller, Wolfgang |
| contents | We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding solutions to the Einstein and soliton equations, there exist solutions near the singular orbit, unique up to a finite number of constants. In part I we make a special assumption that significantly simplifies the proof, and will solve the general case in Part II. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Initial value problems on cohomogeneity one manifolds, I Verdiani, Luigi Ziller, Wolfgang Differential Geometry 53C25, 53C21 We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding solutions to the Einstein and soliton equations, there exist solutions near the singular orbit, unique up to a finite number of constants. In part I we make a special assumption that significantly simplifies the proof, and will solve the general case in Part II. |
| title | Initial value problems on cohomogeneity one manifolds, I |
| topic | Differential Geometry 53C25, 53C21 |
| url | https://arxiv.org/abs/2412.06058 |