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

2022/08/29 by Wei, Zhiqiang, Wu, Yingyi
#32Q15 #53A50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.13359

Abstract

In \citeWeiWu22-3 (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 \citeWeiWu22-3, 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.

Related

• The structure of HCMU metric in a K-Surface
• Linear Weingarten surfaces in Euclidean and hyperbolic space
• The moduli space of HCMU surfaces
• Surfaces and fronts with harmonic-mean curvature one in hyperbolic three-space
• Complex analysis and a class of Weingarten surfaces