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arXiv · 2210.01483

A maximal element of a moduli space of Riemannian metrics

Yuichiro Taketomi
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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.

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Yuichiro Taketomi. 2022-10-04. A maximal element of a moduli space of Riemannian metrics. https://arxiv.org/abs/2210.01483

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