Revolution Surfaces with Constant Mean Curvature in Non-Euclidean Spaces

In this article, we study the conformal mean curvature equation in Thurston’s geometries of Sol space. The classification of revolution surfaces with mean curvature was obtained by studying the corresponding profile curves in Sol space. According to the characteristics of the conformal metric, the revolution surfaces in Sol manifold were obtained through a profile curve revolving respectively. Assumes that the mean curvatures of these revolution surfaces were certain functions, the corresponding differential equations about the profile curves can be obtained. By solving these differential equations, the classification of the revolution surfaces with conformal mean curvature was achieved.