Turiel, F. J. An elementary proof of a Lima’s theorem for surfaces. (English) Zbl 0698.57011 Publ. Mat., Barc. 33, No. 3, 555-557 (1989). 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. Cited in 4 Documents 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 Keywords:action of \({\mathbb{R}}^ n\) on a compact connected surface without boundary; Euler-Poincaré characteristic; fixed point PDFBibTeX XMLCite \textit{F. J. Turiel}, Publ. Mat., Barc. 33, No. 3, 555--557 (1989; Zbl 0698.57011) Full Text: DOI EuDML