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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.04351 |
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| _version_ | 1866909825854603264 |
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| author | Andrade, João H. Case, Jeffrey S. Piccione, Paolo Wei, Juncheng |
| author_facet | Andrade, João H. Case, Jeffrey S. Piccione, Paolo Wei, Juncheng |
| contents | We show that there are infinitely many pairwise nonhomothetic, complete, periodic metrics with constant scalar curvature that are conformal to the round metric on $S^n\setminus S^k$, where $k < \frac{n-2}{2}$. These metrics are obtained by pulling back Yamabe metrics defined on products of $S^{n-k-1}$ and compact hyperbolic $(k+1)$-manifolds. Our main result proves that these solutions are generically distinct up to homothety. The core of our argument relies on classical rigidity theorems due to Obata and Ferrand, which characterize the round sphere by its conformal group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonhomothetic complete periodic metrics with constant scalar curvature Andrade, João H. Case, Jeffrey S. Piccione, Paolo Wei, Juncheng Differential Geometry Analysis of PDEs We show that there are infinitely many pairwise nonhomothetic, complete, periodic metrics with constant scalar curvature that are conformal to the round metric on $S^n\setminus S^k$, where $k < \frac{n-2}{2}$. These metrics are obtained by pulling back Yamabe metrics defined on products of $S^{n-k-1}$ and compact hyperbolic $(k+1)$-manifolds. Our main result proves that these solutions are generically distinct up to homothety. The core of our argument relies on classical rigidity theorems due to Obata and Ferrand, which characterize the round sphere by its conformal group. |
| title | Nonhomothetic complete periodic metrics with constant scalar curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04351 |