On Klein Surfaces with 2p or 2p+2 Automorphisms

On Riemann surfaces of genus g with 4g automorphisms

“…For cyclic groups there are some cases where the order of the group determines the Riemann surface (see [16], [19], [14]). Analogous results are known for Klein surfaces: [4], [7], [8] and [3].…”

On non-orientable Riemann surfaces with 2p or 2p + 2 automorphisms

“…Define γ = p if p is odd or p + 1 if p is even. Let W denote a non-orientable Riemann surface of algebraic genus p which admits a group G of automorphisms of order 2γ and let its corresponding NEC group Γ have signature (6). Let Λ denote an NEC group such that Γ Λ, G ∼ = Λ/Γ, and X/G = U/Λ.…”

“…We explicitly determine the symmetry which yields each Klein surface and give explicit equations for the automorphism group of order 2p or 2(p + 1). This work, in conjunction with the examination of bordered Klein surfaces in [6], provides an extensive analysis of all Klein surfaces which admit automorphism groups of order 2(p + 1) or 2p.…”

Riemann surfaces with real forms which have maximal cyclic symmetry

“…In addition, [9,10]). Hence, the Klein surfaces we are dealing with have topological types 0, 1, or g + 1.…”