Analytic actions on compact surfaces and fixed points (Q1566321)

Let \(G\) be a connected Lie group with a real analytic action on a compact connected surface whose Euler characteristic is non-zero. The author shows that if the action is fixed-point free then the Euler characteristic is greater than or equal to one. In this situation he also shows that the Lie algebra of \(G\) is one of: \(sl(2, {\mathbb R})\), \(o(3)\), \(sl(2, {\mathbb C})\), \(sl(3, {\mathbb R})\) or a subalgebra of the affine algebra of \({\mathbb R}^{2}\) given by the extension of the ideal of constant vector fields by an irreducible linear subalgebra.