A new approach to timelike surfaces which contain inclined curves as geodesics (Q2686636)

Let a timelike surfaces is such that one of the principal curvatures is identically constant, have diagonalizable shape operators in \(\mathbb E_1^3\). Then authors give some results about such surfaces on which inclined curves lie as geodesic curves. The main result of this article is the following. Let \(M\) be a timelike surface in \(\mathbb E_1^3\) whose one of the principal curvatures is identically constant. If \(M\) has a geodesic curve \(\gamma\) which makes a fixed angle with one of the parameter curves, then \(M\) is either a plane, a pseudosphere or a Lorentzian cylinder.