Conformal CMC-surfaces in Lorentzian space forms

Let Q(3) be the common conformal compactification space of the Lorentzian space forms R-1(3), S-1(3) and H-1(3). We study the conformal geometry of space-like surfaces in Q(3). It is shown that any conformal CMC-surface in Q(3) must be conformally equivalent to a constant mean curvature surface in R-1(3), S-1(3) or H-1(3) . We also show that if x : M -> Q(3) is a space-like Willmore surface whose conformal metric g has constant curvature K, then either K = -1 and x is conformally equivalent to a minimal surface in R-1(3), or K = 0 and x is conformally equivalent to the surface H-1(1/root 2) x H-1(1/root 2) in H-1(3).MathematicsSCI(E)中国科技核心期刊(ISTIC)中国科学引文数据库(CSCD)0ARTICLE3299-3102