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