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| Conformal CMC-Surfaces in Lorentzian Space Forms |
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Citation： |
Changxiong NIE.Conformal CMC-Surfaces in Lorentzian Space Forms[J].Chinese Annals of Mathematics B,2007,28(3):299~310 |
| Page view： 1244
Net amount： 801 |
Authors： |
Changxiong NIE; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No. 10125105) and the Research Fund for the Doctoral Program of Higher Education. |
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| Abstract： |
Let $\Q^3$ be the common conformal compactification space of the Lorentzian space forms $\R^3_1$, $\S^3_1$ and $\H^3_1$. 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 $\R^3_1$, $\S^3_1$ or $\H^3_1$. We also show that if $x: M\to\Q^3$ 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 $\R^3_1$, or $K=0$ and $x$ is conformally equivalent to the surface
$\H^1(\frac{1}{\sqrt{2}})\times \H^1(\frac{1}{\sqrt{2}})$ in $\H^3_1$. |
Keywords： |
Conformal geometry, Willmore surfaces, Lorentzian space |
Classification： |
53A30, 53B30 |
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