论文标题
坐标有限型高斯地图的二次表面
Quadric surfaces of coordinate finite type Gauss map
论文作者
论文摘要
我们研究了三维欧几里得空间中的二次表面，该空间是坐标有限型高斯的映射，相对于第二个基本形式$ ii $，即他们的高斯映射向量$ \ boldsymbol {n} $满足关系$Δ^^^{ii}} $ ther $δ^{ii} $表示表面的第二个基本形式$ ii $和$ \ varlambda $的拉普拉斯操作员是第3订单的正方形矩阵。我们表明，螺旋体和球形是上面提到的唯一满足$Δ^^{II} \ boldsymbol的表面类别的类别。
We study quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type Gauss map with respect to the second fundamental form $II$, i.e., their Gauss map vector $\boldsymbol{n}$ satisfies the relation $Δ^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$, where $Δ^{II}$ denotes the Laplace operator of the second fundamental form $II$ of the surface and $\varLambda$ is a square matrix of order 3. We show that helicoids and spheres are the only class of surfaces mentioned above satisfying $Δ^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$.
