Curvature functions on Lorentz 2-manifolds

John Thomas Burns

Vol. 70 (1977), No. 2, 325–335

DOI: 10.2140/pjm.1977.70.325

Abstract

0. Introduction. This paper deals with the problem of describing those functions which can arise as Gaussian curvatures on 2-dimensional Lorentz manifolds, specifically, the 2-dimensional torus T² and the plane R². It is well known that the only compact connected oriented 2-dimensional manifold which admits a Lorentz metric is the torus T², so restricting attention to T² represents no loss in generality.

Mathematical Subject Classification 2000

Primary: 53C50

Secondary: 35L60, 58G99

Milestones

Received: 8 December 1976

Published: 1 June 1977