Proper Biconservative immersions into the Euclidean space

Abstract

In this paper, using the framework of equivariant differential geometry, we study proper $SO(p+1)\times SO(q+1)$-invariant biconservative hypersurfaces into the Euclidean space ${\mathbb{R}}^n$ ($n=p+q+2$) and proper $SO(p+1)$-invariant biconservative hypersurfaces into the Euclidean space ${\mathbb{R}}^n$ ($n=p+2$). Moreover, we show that, in these two classes of invariant families, there exists no proper biharmonic immersion.

20 pages, 3 figures

References in corpus (1)

• Biharmonic PNMC Submanifolds in Spheres

Cited by in corpus (1)

• CMC biconservative surfaces in ${\mathbb{S}}^n\times \mathbb{R}$ and ${\mathbb{H}}^n\times \mathbb{R}$