Compact Einstein-type manifolds with parallel Ricci tensor
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929264622829568 |
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| author | Andrade, Maria Baltazar, Halyson Queiroz, Christopher |
| author_facet | Andrade, Maria Baltazar, Halyson Queiroz, Christopher |
| contents | In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact Einstein-type manifolds with parallel Ricci tensor Andrade, Maria Baltazar, Halyson Queiroz, Christopher Differential Geometry Primary 53C25, 53C20, 53C21, Secondary 53C65 In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures. |
| title | Compact Einstein-type manifolds with parallel Ricci tensor |
| topic | Differential Geometry Primary 53C25, 53C20, 53C21, Secondary 53C65 |
| url | https://arxiv.org/abs/2403.02447 |