论文标题
在旋转表面上的旋转表面，在3维设立空间中具有Weingarten条件
On rotational surfaces in 3 dimensional de Sitter space with Weingarten condition
论文作者
论文摘要
在本文中，我们研究了3-维的固定空间$ \ mathbb {s}^3_1 $在4-维Minkosional Minkowski Space $ \ Mathbb的正交转换下，是常规曲线的轨道，这是常规曲线的轨道 固定的。我们确定通过主曲率参数化的此类Weingarten旋转表面的轮廓曲线。然后，我们将$ \ mathbb {s}^3_1 $与主要曲率$κ$和$λ$满足$κ=Aλ+b $或$κ=aλ+b $或$κ=Aλ^m $的主要曲率$κ$和$λ$对$ \ mathbb {s}^3_1 $进行分类。
In this article, we study spacelike and timelike rotational surfaces in a 3--dimensional de Sitter space $\mathbb{S}^3_1$ which are the orbit of a regular curve under the action of the orthogonal transformation of 4--dimensional Minkowski space $\mathbb{E}^4_1$ leaving a spacelike, a timelike or a degenerate plane pointwise fixed. We determine the profile curve of such Weingarten rotational surfaces parameterized by the principal curvature. Then, we classify spacelike and timelike Weingarten rotational surface in $\mathbb{S}^3_1$ with the principal curvatures $κ$ and $λ$ satisfying $κ=aλ+b$ or $κ=aλ^m$ for special cases of constants $a, b$ and $m$.
