Constant positive 2-mean curvature hypersurfaces (Q1850242)

Hypersurfaces of constant 2-mean curvature in spaces of constant sectional curvature are known to be solutions to a variational problem. The author of the present paper extends this characterization to ambient spaces which are Einstein. Next, the 2-mean curvature of certain hypersurfaces in Einstein manifolds, is estimated. A consequence of the estimation is a generalization of a result, first proved by Chern, showing that there are no complete graphs in the Euclidean space with positive constant 2-mean curvature.