论文标题
关于空间形式的封闭双守护表面的存在
On the Existence of Closed Biconservative Surfaces in Space Forms
论文作者
论文摘要
riemannian 3空间形式的均保守表面$ n^3（ρ）$，是恒定的平均曲率（CMC）表面，或者旋转线性线性的Weingarten表面验证关系$3κ__1+κ__2= 0 $之间的主要曲率$κ_1$和$κ_1$和$κ_______2$。我们将非CMC双向辅助表面的轮廓曲线表征为合适的曲率能量的临界曲线。此外，使用这种表征，我们证明存在一个离散的双映射家族封闭的家族，即没有边界的紧凑型，在3季度圆形的$ s^3（ρ）$中，非CMC双守护式表面。但是，这些封闭的表面均未嵌入$ s^3（ρ）$中。
Biconservative surfaces of Riemannian 3-space forms $N^3(ρ)$, are either constant mean curvature (CMC) surfaces or rotational linear Weingarten surfaces verifying the relation $3κ_1+κ_2=0$ between their principal curvatures $κ_1$ and $κ_2$. We characterise the profile curves of the non-CMC biconservative surfaces as the critical curves for a suitable curvature energy. Moreover, using this characterisation, we prove the existence of a discrete biparametric family of closed, i.e. compact without boundary, non-CMC biconservative surfaces in the round 3-sphere, $S^3(ρ)$. However, none of these closed surfaces is embedded in $S^3(ρ)$.
