Biconservative ideal hypersurfaces in Euclidean spaces

A biconservative submanifold of a Riemannian manifold is a sub-manifold with divergence free stress-energy tensor with respect to bienergy. These are generalizations of biharamonic submanifolds. In 2013, B.Y. Chen and M.I. Munteanu proved that δ(2)-ideal and δ(3)-ideal biharmonic hypersurfaces in Euclidean space are minimal. In this paper, we generalize this result for δ(2)-ideal and δ(3)-ideal bisonservative hypersurfaces in Euclidean space. Also, we study δ(4)-ideal biconservative hypersurfaces in Euclidean space E6 having constant scalar curvature. We prove that such a hypersurface must be of constant mean curvature.