Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909899002216448 |
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| author | Samani, Elahe Khalili Mouillé, Lawrence |
| author_facet | Samani, Elahe Khalili Mouillé, Lawrence |
| contents | We explore existence of invariant metrics with positive intermediate Ricci curvature on closed, low-dimensional cohomogeneity one manifolds. For a certain cohomogeneity one $\mathsf{Spin}(4)$-action on $S^3 \times \mathbb{C}\mathrm{P}^2$, we construct an invariant metric with positive 4th-intermediate Ricci curvature and show it cannot admit one with positive 3rd-intermediate Ricci curvature. We further establish similar symmetry obstructions to positive curvature for $S^3 \times S^3$, $S^3 \times S^4$, and several families of cohomogeneity one manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions Samani, Elahe Khalili Mouillé, Lawrence Differential Geometry 53C20, 57S15 We explore existence of invariant metrics with positive intermediate Ricci curvature on closed, low-dimensional cohomogeneity one manifolds. For a certain cohomogeneity one $\mathsf{Spin}(4)$-action on $S^3 \times \mathbb{C}\mathrm{P}^2$, we construct an invariant metric with positive 4th-intermediate Ricci curvature and show it cannot admit one with positive 3rd-intermediate Ricci curvature. We further establish similar symmetry obstructions to positive curvature for $S^3 \times S^3$, $S^3 \times S^4$, and several families of cohomogeneity one manifolds. |
| title | Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions |
| topic | Differential Geometry 53C20, 57S15 |
| url | https://arxiv.org/abs/2507.17920 |