Symmetries of Accola-Maclachlan and Kulkarni surfaces

Symmetries of Accola-maclachlan and Kulkarni Surfaces

For all g ≥ 2 there is a Riemann surface of genus g whose automorphism group has order 8g+8, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola and Maclachlan established the existence of such surfaces; we shall call them Accola-Maclachlan surfaces. Later Kulkarni proved that for sufficiently large g the Accola-Maclachlan surface was unique for...

One-dimensional families of Riemann surfaces of genus g with 4g+4automorphims

We prove that the maximal number ag + b of automorphisms of equisymmetric and complex-uniparametric families of Riemann surfaces appearing in all genera is 4g+ 4. For each integer g ≥ 2 we find an equisymmetric complex-uniparametric family Ag of Riemann surfaces of genus g having automorphism group of order 4g + 4. For g ≡ −1mod4 we present another uniparametric family Kg with automorphism grou...

Symmetries of Curves and Surfaces

Symmetries of microcanonical entropy surfaces

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical...

Symmetries of canal surfaces and Dupin cyclides

We develop a characterization for the existence of symmetries of canal surfaces defined by a rational spine curve and rational radius function. In turn, this characterization inspires an algorithm for computing the symmetries of such canal surfaces. For Dupin cyclides in canonical form, we apply the characterization to derive an intrinsic description of their symmetries and symmetry groups, whi...