4-dimensional Space forms as determined by the volumes of small geodesic balls
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914768386785280 |
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| author | Park, JeongHyeong |
| author_facet | Park, JeongHyeong |
| contents | Gray-Vanhecke conjectured that the volumes of small geodesic balls could determine if the manifold is a space form, and provided a proof for the compact 4-dimensional manifold, and some cases. In this paper, similar results for the 4-dimensional case are obtained, based upon tensor calculus and classical theorems rather than the topological characterizations in [6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 4-dimensional Space forms as determined by the volumes of small geodesic balls Park, JeongHyeong Differential Geometry 53C21, 53B20 Gray-Vanhecke conjectured that the volumes of small geodesic balls could determine if the manifold is a space form, and provided a proof for the compact 4-dimensional manifold, and some cases. In this paper, similar results for the 4-dimensional case are obtained, based upon tensor calculus and classical theorems rather than the topological characterizations in [6]. |
| title | 4-dimensional Space forms as determined by the volumes of small geodesic balls |
| topic | Differential Geometry 53C21, 53B20 |
| url | https://arxiv.org/abs/2404.15665 |