On extremal properties of compact parabolic surfaces in a Riemannian space

The structure of parabolic surfaces in a Riemannian space is studied. Conditions are determined for compact parabolic surfaces to be totally geodesic.
The proof uses the normal bundle of the surface with the Sasaki metric. A differentiable horizontal distribution arises on this bundle. It is proved that the distribution is holonomic and totally geodesic.
Bibliography: 23 titles.