2015/10/05 by Christophe Bavard, Bavard, Christophe, Pierre Mounoud +1
Mathematics · #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1510.01253
openalex publication_date 2015/10/05 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We study the simply connected inextendable Lorentzian surfaces admitting a\nKilling vector field. We construct a natural family of such surfaces, that we\ncall "universal extensions". They are characterized by a condition of symmetry,\nthe "reflexivity", and a by a rather weak completeness assumption, the absence\nof "saddles at infinity". Considering these surfaces as model spaces, we study\ntheir minimal quotients, divisible open sets and conjugate points. We show\nuniformisation results (by an open subset of one of these universal extensions,\nwhich is uniquely determined) in the following cases: compact surfaces and\nanalytical surfaces. It allows us to give a classification of Lorentzian tori\nand Klein bottles with a Killing vector field.\n