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An elementary proof of a Lima’s theorem for surfaces. (English) Zbl 0698.57011

Summary: Theorem. Let M be a compact connected surface without boundary. Consider a \(C^{\infty}\) action of \({\mathbb{R}}^ n\) on M. Then, if the Euler- Poincaré characteristic of M is not zero there exists a fixed point.

MSC:

57S20 Noncompact Lie groups of transformations
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
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