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Mathematics > Differential Geometry

arXiv:2210.01483 (math)
[Submitted on 4 Oct 2022]

Title:A maximal element of a moduli space of Riemannian metrics

Authors: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.
Subjects: Differential Geometry (math.DG)
MSC classes: 53C30, 22E25, 53C25
Cite as: arXiv:2210.01483 [math.DG]
  (or arXiv:2210.01483v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2210.01483

Submission history

From: Yuichiro Taketomi [view email]
[v1] Tue, 4 Oct 2022 09:18:48 UTC (62 KB)
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