Conformally weighted Einstein manifolds: the uniqueness problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910908452700160 |
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| author | Brozos-Vázquez, Miguel García-Río, Eduardo Mojón-Álvarez, Diego |
| author_facet | Brozos-Vázquez, Miguel García-Río, Eduardo Mojón-Álvarez, Diego |
| contents | We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped products. Secondly, a global classification result is obtained when one of the underlying metrics is complete, showing that either it is a weighted space form, a special Einstein warped product, or a specific family of quasi-Einstein warped products. As a consequence, it must be a weighted sphere in the compact case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformally weighted Einstein manifolds: the uniqueness problem Brozos-Vázquez, Miguel García-Río, Eduardo Mojón-Álvarez, Diego Differential Geometry 53C21 53B20 53C18 53C24 53C25 We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped products. Secondly, a global classification result is obtained when one of the underlying metrics is complete, showing that either it is a weighted space form, a special Einstein warped product, or a specific family of quasi-Einstein warped products. As a consequence, it must be a weighted sphere in the compact case. |
| title | Conformally weighted Einstein manifolds: the uniqueness problem |
| topic | Differential Geometry 53C21 53B20 53C18 53C24 53C25 |
| url | https://arxiv.org/abs/2504.07860 |