Gaussian curvatures of Lorentzian metrics on the plane and punctured planes
Author: Jiang Fan Li
Journal: Proc. Amer. Math. Soc. 108 (1990), 197-205
MSC: Primary 53C50; Secondary 35J60
MathSciNet review: 984805
Abstract: We prove that every is the Gaussian curvature of some -Lorentzian metric . Let denote the cylinder. We prove that every continuous function on is the Gaussian curvature of some -Lorentzian metric. If satisfies the condition (H) in the Lemma 2 below, then it is the curvature function of some -Lorentzian metric. If has compact support, then the Lorentzian metric can be made complete.
Keywords: Curvature function, (complete) Lorentzian metric, characteristic line, (forward) complete geodesic
Article copyright: © Copyright 1990 American Mathematical Society