The splitting and deformations of the generalized Gauss map of compact CMC surfaces
The study of constant mean curvature surfaces in the 3-sphere, which are often called CMC surfaces, has a long and interesting development and it continues to attract the attention of differential geometers. In the paper under review, the author proves that the generalized Gauss map of CMC surfaces in the 3-sphere globally splits into two non-conformal harmonic maps into the 2-sphere. As a corollary of this result, it is proved that a full superconformal minimal surface in \(S^{4m}\) cannot be isometric to a minimal surface in the 3-sphere \(S^3\), which gives a partial answer to Lawson's conjecture.
scientific article; zbMATH DE number 1321872
scientific article