Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds

Abstract

After obtaining an explicit description in coordinates of invariant metrics on four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds, for each of these spaces we completely describe Killing and geodesic vector fields and homogeneous geodesics through a point. In particular, this allows us to determine explicit examples of four-dimensional non-reductive pseudo-Riemannian g.o. spaces. Finally, we determine the possible holonomy Lie algebras of the invariant metrics.