Isometric rigidity of $L^2$-spaces with manifold targets

David Lenze

Isometric rigidity of $L^2$-spaces with manifold targets

Metric Geometry 2025-04-10 v3 Differential Geometry

Authors: David Lenze

Abstract

We describe the isometry group of $L^2(\Omega, M)$ 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 $\Omega$ and a family of isometries of $M$ , distinguishing these spaces from the classical $L^2(\Omega)$ . Additionally, we prove that these spaces lack irreducible factors and that two such spaces are isometric if and only if the underlying manifolds are.

Keywords

isometric rigidity L^2 spaces manifold targets isometry group Riemannian manifolds irreducible universal cover automorphism

Cite

@article{arxiv.2412.13914,
  title  = {Isometric rigidity of $L^2$-spaces with manifold targets},
  author = {David Lenze},
  journal= {arXiv preprint arXiv:2412.13914},
  year   = {2025}
}

Comments

25 pages. To appear in Trans. Amer. Math. Soc.; revised based on referee's comments

Isometric rigidity of $L^2$-spaces with manifold targets

Abstract

Keywords

Cite

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