摘要
Let Q^3 be the common conformal compactification space of the Lorentzian space forms Q^3 1 ,S^3 1,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^3 1,or,H^3 1,We also show that if x ：M→Q^3 is a space-like Willmore surface whose conformal metric g has constant curvature K,the either K = -1 and x is conformally equivalent to a minimal surface in R^3 1,or K=0 and x is conformally equivalent to the surface H^1（1/√2）×H^1（1/√2） in H^3 1.
基金
the National Natural Science Foundation of China (No. 10125105)
the Research Fund for the Doctoral Program of Higher Education.
