Semi-parallel surfaces in Euclidean space (Q1068369)

The paper gives a classification of semi-parallel surface immersions into Euclidean space. Here an isometric immersion \(i: M\to \tilde M\) between Riemannian manifolds is called semi-parallel iff \(\bar R(X,Y)\cdot h=0\) for all tangent vectors X,Y to M where h denotes the second fundamental form and \(\bar R\) the curvature tensor of the van der Waerden-Bortolotti connection of i. In addition it is shown that the totally geodesic immersions are the only minimal semi-parallel immersions into a Euclidean space.