Minkowski空间中的类时Salkowski曲线和反Salkowski曲线
Time-like Salkowski and anti-Salkowski curves in Minkowski space $\e_1^3$
摘要：
Salkowski \cite{salkow}在一个世纪前在欧氏空间$\e^3$中引入了一类常曲率非常挠率曲线（Salkowski曲线）和一类常挠率非常曲率曲线（anti-Salkowski曲线）。本文将这类曲线的定义推广到三维Minkowski空间$\e_1^3$中的类时曲线。之后，我们在Minkowski空间$\e_1^3$中引入了类时Salkowski曲线和类时Anti-Salkowski曲线的显式参数化.并将其刻画为具有常曲率或常挠率且其法向量与固定直线成常角的空间曲线。
英文摘要：
Salkowski \cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space $\e^3$. In this paper, we adapt definition of such curves to time-like curves in Minkowski 3-space $\e_1^3$. Thereafter, we introduce an explicit parametrization of a time-like Salkowski curves and a time-like Anti-Salkowski curves in Minkowski space $\e_1^3$. Also, we characterize them as space curve with constant curvature or constant torsion and whose normal vector makes a constant angle with a fixed line.
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