In this paper, we mainly study the isometric deformation preserving principal curvature of surfaces in Minkowski space R13. By generalizing some concepts from R3 to R13, we find these conclusions drawn by O. Bonnet or S. S. Chern are still hold in R13. Moreover, we research the new case that the gradient of mean curvature is null and get some meaningful results , of which main conclusion is that non-flat surfaces that can be isometrically deformed preserving the principal curvature is certainly not W-surface. |