Constant mean curvature surfaces in 4-space forms
The authors study existence and uniqueness for isometric immersions between a fixed simply connected Riemannian surface and a fixed 4- dimensional space form of curvature c, which have a parallel mean curvature vector. A typical theorem: There exists such an immersion with \(H>0\), if and only if \(K\leq c+H\) 2, and the function \(a=(c+H\) \(2- K)^{1/2}\) is of absolute value type with \(\Delta\) log a\(=2K\). Up to local congruences, all these form a two parameter family.
scientific article; zbMATH DE number 4063951
scientific article