轨道空间等距映射的提升
度量几何
2021-09-17 v2 微分几何
表示论
摘要
给定一个紧群的正交表示，我们证明轨道空间等距群连通分支中的任意元素均可提升为原欧几里得空间上的等变等距映射。推论包括该连通分支的一个简单公式，其适用于“大多数”表示。
引用
@article{arxiv.2004.00097,
title = {Lifting isometries of orbit spaces},
author = {Ricardo A. E. Mendes},
journal= {arXiv preprint arXiv:2004.00097},
year = {2021}
}
备注
9 pages. Final version, to appear in the Bulletin of the London Mathematical Society. Compared to the previous version, one of the corollaries to the main result has been reformulated as an easy-to-use formula (Proposition 5(b)). Moreover, many improvements to the presentation have been made, including the addition of a new section (Section 2)