Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed point free involutions on Riemann surfaces   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.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org