Bonnet Surface with Parallel Mean Curvature Direction in R4(C)

Abstract:

      In this paper, we study the Bonnet surfaces in the 4-dim space forms, which admit an isometric deformation preserving the mean curvature function. When the mean curvature direction is parallel, we first parameterize the Bonnet surfaces in R⁴(C) by semi-geodesic isothermal parameters, and then obtain a classification result which generalizes some work in [5] by W.H.Chen and H.Z.Li.