Realization of HCMU metrics in 3-dimensional space forms as Weingarten surfaces

Zhiqiang Wei; Yingyi Wu

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arXiv · 2208.13359

Realization of HCMU metrics in 3-dimensional space forms as Weingarten surfaces

Zhiqiang Wei·Yingyi Wu

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Abstract

In \cite{WeiWu22-3} (J.Geom.Anal.32, 199(2022)), we classified HCMU surfaces in 3-dimensional Euclidean space as Weingarten surfaces by holomorphic functions. In this paper, using a totally different method from \cite{WeiWu22-3}, we will classify HCMU surfaces in 3-dimensional space forms as Weingarten surfaces. Moreover we will give a criteria of a Weingarten surface which is also an HCMU surface.

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Zhiqiang Wei, Yingyi Wu. 2022-08-29. Realization of HCMU metrics in 3-dimensional space forms as Weingarten surfaces. https://arxiv.org/abs/2208.13359

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