Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics

A. O. Remizov, F. Tari

Published 2015-05-25Version 1

We consider a pseudo-Riemannian metric that changes signature along a smooth curve on a surface, called the discriminant curve. The discriminant curve separates the surface locally into a Riemannian and a Lorentzian domain. We study the local behaviour and properties of geodesics at a point on the discriminant where the isotropic direction is tangent to the discriminant curve.