Spherical Chen surfaces which are mass-symmetric and of 2-type (Q1107833)

The main result of this paper is the classification of spherical, mass- symmetric, 2-type Chen surfaces. The main result is stated as follows. Theorem. Let M be a mass-symmetric, 2-type Chen surface in a hypersphere S m of \(E^{m+1}\). Then M is either pseudo-umbilical or flat. If M is flat and not pseudo-umbilical, then M lies fully in a totally geodesic 3- sphere, or in a totally geodesic 5-sphere, or in a totally geodesic 7- sphere. In addition, the author constructs many examples of mass- symmetric, spherical, 2-type Chen surfaces.