A loop group method for Demoulin surfaces in the 3-dimensional real projective space

Abstract

A natural Gauss map for a surface in the 3-dimensional real projective space P3 will be defined and called the first-order Gauss map. It will be shown that the first-order Gauss map is conformal if and only if it is a Demoulin surface, which is a special case among projective minimal surfaces. Moreover, it will be shown that the first-order Gauss map is Lorentz harmonic if and only if it is a Demoulin surface or a projective minimal coincidence surface. We also characterize the surfaces via a family of flat connections on the trivial bundle D×SL4R over a simply connected domain D in the Euclidean 2-plane.