Helicoidal Maximal Surfaces in Lorentz-Minkowski Space

Abstract

We investigate helicoidal surfaces in Lorentz-Minkowski space . A purely geometric method is used for classifying the helicoidal maximal surfaces. This description consists on exposing helicoidal maximal surfaces as solutions to certain adequate Bjorling problems in , and shows that a maximal surface is helicoidal if and only if it lies in the associate family of a catenoid in . We shall also give characteristic properties of the catenoids and helicoids in .