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Null helices in Lorentzian space forms. (English) Zbl 1003.53052
At first, for a null curve in an $n$-dimensional Lorentzian space form the authors introduce a Frenet frame with the minimum number of curvature functions (which they call the Cartan frame), and study next the null helices in those spaces, that is, null curves with constant curvatures. Secondly, the authors find a complete classification of these curves in the Lorentzian space forms of low dimensions: the five-dimensional Lorentz-Minkowski space $\Bbb R^5_1$, the four-dimensional De Sitter space-time $\Bbb S^4_1$ and four-dimensional anti-De Sitter space-time $\Bbb H^4_1$. The main theorems of this paper state that in $\Bbb R^5_1$ there are three different families of helices, in $\Bbb S^4_1$ there is only one type of helices and in $\Bbb H^4_1$ one can find up to nine distinct types of helices.

##### MSC:
 53C50 Lorentz manifolds, manifolds with indefinite metrics 53C80 Applications of global differential geometry to physics
##### Keywords:
Lorentzian space form; Cartan frame; null helix; Frenet frame
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