论文标题
坐标有限II型的表面
Surfaces of coordinate finite II-type
论文作者
论文摘要
在本文中，我们研究了三维欧几里得空间中的革命表面类别$ e^{3} $，其位置向量$ \ boldsymbol {x} $满足条件$Δ^{ii} \ boldsymbol {ii} \ boldsymbol {x} = a \ boldsymbol { $δ^{ii} $表示表面的第二个基本形式$ II $的拉普拉斯操作员。我们表明，满足前面关系的革命表面是链球菌或球体的一部分。
In this article, we study the class of surfaces of revolution in the 3-dimensional Euclidean space $E^{3}$ with nonvanishing Gauss curvature whose position vector $\boldsymbol{x}$ satisfies the condition $Δ^{II}\boldsymbol{x}=A\boldsymbol{x}$, where $A$ is a square matrix of order 3 and $Δ^{II}$ denotes the Laplace operator of the second fundamental form $II$ of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.
