부산대학교 도서관

Let $\Bbb{L}^3$ be the 3-dimensional Lorentz space, i.e., the Euclidean 3-space $\Bbb{R}^3$ equipped with the metric $g\coloneq (-,+,+)$ and let $\gamma$ be a lightlike (null) curve in $\Bbb{L}^3$. It is well known that $\gamma$ can be parameterised by the pseudo-arc, i.e., $g(\gamma'', \gamma'')=1$ and then $F=\{\gamma', N, \gamma''\}$ is a distinguished Frenet frame along $\gamma$, where $N$ is lightlike and $g(\gamma', N)=1$. In the paper under review $\gamma$ is said to be a null slant helix if there exists a fixed direction $V$ such that $g(V, \gamma'')={\rm constant}$. Then it is shown that the only null slant helices are the null ones. After giving some examples in $\Bbb{L}^3$, the authors state the same question in $\Bbb{L}^4$, showing that here there exist no null slant helices.