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

Abstract

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.

References in corpus (2)

• Geodesics on an ellipsoid in Minkowski space
• On the local and global properties of geodesics in pseudo-Riemannian metrics

Cited by in corpus (3)

• Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint
• On solutions of singular differential equations of the second order
• Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds