Compact harmonic RCD$(K, N)$ spaces are harmonic manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908588211961856 |
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| author | Huang, Zhangkai |
| author_facet | Huang, Zhangkai |
| contents | In this paper, we study harmonic RCD$(K,N)$ spaces as the counterpart of harmonic Riemannian manifolds with Ricci curvature bounded from below. We prove that a compact RCD$(K,N)$ space is isometric to a smooth closed Riemannian manifold if it satisfies either of the following harmonicity conditions:(1) the heat kernel $ρ(x,y,t)$ depends only on the variable $t$ and the distance between points $x$ and $y$; (2) the volume of the intersection of two geodesic balls depends only on their radii and the distance between their centers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact harmonic RCD$(K, N)$ spaces are harmonic manifolds Huang, Zhangkai Differential Geometry Metric Geometry 28A75 In this paper, we study harmonic RCD$(K,N)$ spaces as the counterpart of harmonic Riemannian manifolds with Ricci curvature bounded from below. We prove that a compact RCD$(K,N)$ space is isometric to a smooth closed Riemannian manifold if it satisfies either of the following harmonicity conditions:(1) the heat kernel $ρ(x,y,t)$ depends only on the variable $t$ and the distance between points $x$ and $y$; (2) the volume of the intersection of two geodesic balls depends only on their radii and the distance between their centers. |
| title | Compact harmonic RCD$(K, N)$ spaces are harmonic manifolds |
| topic | Differential Geometry Metric Geometry 28A75 |
| url | https://arxiv.org/abs/2412.20841 |