A maximal element of a moduli space of Riemannian metrics
Differential Geometry
2022-10-05 v1
Abstract
For a given smooth manifold, we consider the moduli space of Riemannian metrics up to isometry and scaling. One can define a preorder on the moduli space by the size of isometry groups. We call a Riemannian metric that attains a maximal element with respect to the preorder a maximal metric. Maximal metrics give nice examples of self-similar solutions for various metric evolution equations such as the Ricci flow. In this paper, we construct many examples of maximal metrics on Euclidean spaces.
Cite
@article{arxiv.2210.01483,
title = {A maximal element of a moduli space of Riemannian metrics},
author = {Yuichiro Taketomi},
journal= {arXiv preprint arXiv:2210.01483},
year = {2022}
}