论文标题
Minkowski空间中的旋转$ k^α$ - 翻译器
Rotational $K^α$-translators in Minkowski space
论文作者
论文摘要
Minkowski空间中的空间表面$ \ MATHBB {r} _1^3 $称为$ k^α$ - 如果满足$ k^α= \ langle n，\ vec {v}向量字段和$ \ vec {v} $是$ \ mathbb {r} _1^3 $的方向。在本文中，我们对所有旋转$ k^α$ translators进行了分类。该分类将取决于旋转轴的因果特征。尽管$ k^α$流的理论适用于间距表面，但描述$ k^α$ translators的方程式仍然对时间表式表面有效。因此，我们还研究了满足相同规定的高斯曲率方程的及时旋转表面。
A spacelike surface in Minkowski space $\mathbb{R}_1^3$ is called a $K^α$-translator of the flow by the powers of Gauss curvature if satisfies $K^α= \langle N,\vec{v}\rangle$, $α\neq 0$, where $K$ is the Gauss curvature, $N$ is the unit normal vector field and $\vec{v}$ is a direction of $\mathbb{R}_1^3$. In this paper, we classify all rotational $K^α$-translators. This classification will depend on the causal character of the rotation axis. Although the theory of the $K^α$-flow holds for spacelike surfaces, the equation describing $K^α$-translators is still valid for timelike surfaces. So we also investigate the timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation.
