In this paper, we investigate special associated curve of a non-degenerate Frenet curve according to the Sabban frame in anti de Sitter 3-space. Moreover, we give a construction method of Sabban apparatus of a special direction curve in terms of the elements of Sabban apparatus of its donor curve. Furthermore, we obtain some results for the direction curve with respect to special cases of the base curve. Finally, we give an example of a helix and its direction curve which is also a helix and draw theirs images under the stereographic projection in Minkowski 3-space.

In this article, we investigate polynomial helices in the n-dimensional semi-Euclidean space with index two for n ? 4. We obtain some families of spacelike and timelike polynomial helices. These helices have spacelike or timelike or null axes. After that, we give some examples of the spacelike and the timelike polynomial helices in the n-dimensional semi-Euclidean space with index two for n = 4,5 and 6.