Isometric rigidity of $L^2$-spaces with manifold targets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910907222720512 |
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| author | Lenze, David |
| author_facet | Lenze, David |
| contents | We describe the isometry group of $L^2(Ω, M)$ for Riemannian manifolds $M$ of dimension at least two with irreducible universal cover. We establish a rigidity result for the isometries of these spaces: any isometry arises from an automorphism of $Ω$ and a family of isometries of $M$, distinguishing these spaces from the classical $L^2(Ω)$. Additionally, we prove that these spaces lack irreducible factors and that two such spaces are isometric if and only if the underlying manifolds are. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isometric rigidity of $L^2$-spaces with manifold targets Lenze, David Metric Geometry Differential Geometry 51F99, 58D15 We describe the isometry group of $L^2(Ω, M)$ for Riemannian manifolds $M$ of dimension at least two with irreducible universal cover. We establish a rigidity result for the isometries of these spaces: any isometry arises from an automorphism of $Ω$ and a family of isometries of $M$, distinguishing these spaces from the classical $L^2(Ω)$. Additionally, we prove that these spaces lack irreducible factors and that two such spaces are isometric if and only if the underlying manifolds are. |
| title | Isometric rigidity of $L^2$-spaces with manifold targets |
| topic | Metric Geometry Differential Geometry 51F99, 58D15 |
| url | https://arxiv.org/abs/2412.13914 |