Abstract
Consider an effective real analytic action of a connected Lie group G on a compact connected surface of Euler characteristic χ≠0. We show that if the action has no fixed point then χ≥1 and the Lie algebra 𝒢 of G is isomorphic either to a subalgebra of the affine algebra of ℝ2, which is the extension of the ideal of constant vector fields by an irreducible linear subalgebra, or to sl(2,ℝ), o(3), sl(2,ℂ) and sl(3,ℝ).
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Received: 7 August 2001 Published online: 24 January 2003
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Turiel, FJ. Analytic actions on compact surfaces and fixed points. Manuscripta Math. 110, 195–201 (2003). https://doi.org/10.1007/s00229-002-0331-7
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DOI: https://doi.org/10.1007/s00229-002-0331-7