标题： 关于欧几里得空间和双曲空间中的螺旋线的一篇简短注记 显示英文标题

标题： A note on helices in the Euclidean space and in the hyperbolic space

摘要： 我们证明了在欧几里得空间中，与旋转相关的Killing向量场的普遍螺旋线是螺旋线，即具有常曲率和常挠率的曲线。 在双曲空间$\h^3$中，我们得到了与双曲旋转、球面旋转和抛物旋转相关的Killing向量场的螺旋线的参数表示。 证明了这些螺旋线是在$\h^3$的适当曲面上的测地线。 显示英文摘要

摘要： We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $\h^3$, we obtain the parametrization of helices for the Killing vector fields associated to hyperbolic rotations, spherical rotations and parabolic rotations. It is proved that these helices are geodesics in suitable surfaces of $\h^3$.