On pq-hyperelliptic Riemann surfaces

Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ρ for which X/ρ is an orbifold of genus p. Here we classify conformal actions on 2-hyperelliptic Rieman surfaces of genus g > 9, up to topological conjugacy and determine which of them can be maximal.

Research Article Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

On p-hyperelliptic Involutions of Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be phyperelliptic if X admits a conformal involution ρ, called a p-hyperelliptic involution, for which X/ρ is an orbifold of genus p. Here we give a new proof of the well known fact that for g > 4p + 1, ρ is unique and central in the group of all automorphisms of X. Moreover we prove that every two p-hyperelliptic involutions commute for 3p ...

On gonality automorphisms of p-hyperelliptic Riemann surfaces

A compact Riemann surface X of genus g > 1 is said to be a p-hyperelliptic if X admits a conformal involution ρ for which X/ρ has genus p. This notion is the particular case of so called cyclic (q, n)-gonal surface which is defined as the one admitting a conformal automorphism δ of order n such that X/δ has genus q. It is known that for g > 4p + 1, ρ is unique and so central in the automorphism...

Physically Realistic Solutions to the Ernst Equation on Hyperelliptic Riemann Surfaces

A class of solutions to the Ernst equation (the stationary axisymmetric Einstein equations in vacuum) is discussed which is constructed via Riemann–Hilbert techniques on hyperelliptic Riemann surfaces. We identify a physically interesting subclass where the Ernst potential is everywhere regular except at a closed surface which might be identified with the surface of a body of revolution. The co...