紧曲面上超可解李群解析作用的不动点
Fixed points of analytic actions of supersoluble Lie groups on compact surfaces
摘要：
证明了在具有非零欧拉示性数的紧致曲面上的连通超可解李群的每个实解析作用都有一个不动点。这意味着E. Lima在直线的仿射群的$S^2$上的无不动点$C^{\infty}$作用不能用解析作用来近似。一个例子给出了一个分析，不动点自由行动的$S^2$的可解群是不是超可溶的。
英文摘要：
We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free $C^{\infty}$ action on $S^2$ of the affine group of the line cannot be approximated by analytic actions. An example is given of an analytic, fixed point free action on $S^2$ of a solvable group that is not supersoluble.
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