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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.18596 |
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| _version_ | 1866929380006035456 |
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| author | Colombo, Giulio Mariani, Marco Rigoli, Marco |
| author_facet | Colombo, Giulio Mariani, Marco Rigoli, Marco |
| contents | We prove an extension of Eells and Sampson's rigidity theorem for harmonic maps from a closed manifold of non-negative Ricci curvature to a manifold of non-positive sectional curvature. We give an application of our result in the setting of harmonic-Einstein (or Ricci-harmonic) metrics and as a consequence we recover a classical rigidity result of Hamilton for the problem of prescribed positive definite Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sharp Eells-Sampson type theorem under positive sectional curvature upper bounds Colombo, Giulio Mariani, Marco Rigoli, Marco Differential Geometry 53C43, 53C20, 53C21, 53C25 We prove an extension of Eells and Sampson's rigidity theorem for harmonic maps from a closed manifold of non-negative Ricci curvature to a manifold of non-positive sectional curvature. We give an application of our result in the setting of harmonic-Einstein (or Ricci-harmonic) metrics and as a consequence we recover a classical rigidity result of Hamilton for the problem of prescribed positive definite Ricci curvature. |
| title | A sharp Eells-Sampson type theorem under positive sectional curvature upper bounds |
| topic | Differential Geometry 53C43, 53C20, 53C21, 53C25 |
| url | https://arxiv.org/abs/2403.18596 |