Cartan projective connection and geodesic simulation (Q1896715)

The paper contains a proof of the following Theorem: In the ``event space'' \(N \times \mathbb{R}\) of a quasi-geodesic flow \((N,D)\) there exists a (non-unique) generalized projective connection whose geodesic lines are integral curves of the quasi-geodesic flow \(D\). This result is a solution of É. Cartan's problem [see Bull. Soc. Math. Fr. 52, 205-241 (1924 JFM 50.0500.02)].