Curves Along Lorentzian Submersions

Abstract

We explore the impact of curve theory on the characterization of Lorentzian submersions which are special cases of semi-Riemannian submersions. We firstly give a classification of curves according to their causal character along a Lorentzian submersion. Then, we investigate the effects of certain curves, specifically the non-null Frenet curve, the non-null circle, the non-null helix, and the geodesic, under a Lorentzian submersion, and we seek their geometric meaning. Finally, we examine the situation where a Cartan-framed lightlike curve is carried from the total manifold to the base manifold through a Lorentzian submersion. Mathematics Subject Classification (2010): 58D17, 58A05, 53C40, 53C20.