Isometric deformation of surfaces in \(R^ 3\) preserving the mean curvature function (Q915135)

The authors study non-umbilical surfaces in Euclidean space \(R^ 3\) with constant Gaussian curvature, which admit a non-trivial isometric deformation preserving the mean curvature function. After an interesting local analysis for any surface in \(R^ 3\), the authors show that the Gaussian curvature of these surfaces must be zero.