Biconservative ideal hypersurfaces in Euclidean spaces

Abstract

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 $\delta(2)$-ideal and $\delta(3)$-ideal biharmonic hypersurfaces in Euclidean space are minimal. In this paper, we generalize this result for $\delta(2)$-ideal and $\delta(3)$-ideal bisonservative hypersurfaces in Euclidean space. Also, we study $\delta(4)$-ideal biconservative hypersurfaces in Euclidean space $\mathbb{E}^{6}$ having constant scalar curvature. We prove that such a hypersurface must be of constant mean curvature.