Peterson Surfaces

Abstract

Peterson surface is a surface having a conjugate net of conical or cylindrical lines which are the main base of the bending. For example, Monge surfaces with a circular cylindrical directrix surface, the corresponding translation surfaces and surfaces of revolution are Peterson surfaces . The indicatrix of rotations of Peterson surfaces is right conoid. In particular, right helicoid is the indicatrix for carved surface; equilateral hyperbolic paraboloid is the indicatrix for translation surface. First, this class of the surfaces was studied by K.M. Peterson as an example of surfaces assuming bending at the main base. Peterson (1866) has pointed at a class of surfaces capable to bend so that two appointed families of lines remain conjugated during all process of bending. Using his terminology, one may say that these lines are main base of bending for the considered surfaces.