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.

19 pages. arXiv admin note: text overlap with arXiv:1610.03005, arXiv:1412.5479 by other authors

Cited by in corpus (1)

• Biconservative quasi-minimal immersions into semi-Euclidean spaces