论文标题
球体中的封闭双辅助性超曲面
Closed Biconservative Hypersurfaces in Spheres
论文作者
论文摘要
我们将空间$ n^n（ρ）$的非CMC双辅助旋转曲面的曲线曲线描述为$ p $ - 弹性曲线，对于适当的理性数字$ p \ [1/4,1）$中的合理数字$ p \，这取决于环境空间的尺寸$ n $。分析这些$ p $弹性曲线的封闭条件，我们证明了非CMC的离散的双脂肪家族的存在（即无边界的紧凑型）$ \ MATHBB {s}^n（ρ）$中的双辅助性hypersurfaces。这些Hyperfaces都不能嵌入$ \ Mathbb {s}^n（ρ）$中。
We characterise the profile curves of non-CMC biconservative rotational hypersurfaces of space forms $N^n(ρ)$ as $p$-elastic curves, for a suitable rational number $p\in[1/4,1)$ which depends on the dimension $n$ of the ambient space. Analysing the closure conditions of these $p$-elastic curves, we prove the existence of a discrete biparametric family of non-CMC closed (i.e., compact without boundary) biconservative hypersurfaces in $\mathbb{S}^n(ρ)$. None of these hypersurfaces can be embedded in $\mathbb{S}^n(ρ)$.
