On the duality between rotational minimal surfaces and maximal surfaces

Abstract

We investigate the duality between minimal surfaces in Euclidean space and maximal surfaces in Lorentz–Minkowski space in the framework of rotational surfaces. We study if the dual surfaces of two congruent rotational minimal (or maximal) surfaces are congruent. We analyze the duality process when we deform a rotational minimal (maximal) surface by a one-parametric group of rotations. In this context, the family of Bonnet minimal (maximal) surfaces and the Goursat transformations play a remarkable role.