Fixed point free involutions on Riemann surfaces

Details Fixed point free involutions on Riemann surfaces Fixed point free involutions on Riemann surfaces

2005-04-06

arxiv.org/abs/math/0504109v2

Mathematics

Differential Geometry

12 pages, 8 figures

Scientific paper

Involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface $X$ of even genus with an arbitrary Riemannian metric $d$ admitting an involution $\tau$, it is known that $\min_{p\in X}d(p,\tau(p))$ is bounded by a constant which depends on the genus of $X$. The equivalent result is proved to be false in odd genus, and the optimal constant for hyperbolic Riemann surfaces is calculated in genus 2.

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