Classifications of Flat Surfaces with Generalized 1-Type Gauss Map in L-3

Abstract

In this paper, we study surfaces in the Minkowski 3-space L-3, such that Delta G is a linear combination of the Gauss map G and a constant vector C, called generalized 1-type Gauss map. First of all, we prove that all cylindrical surfaces in L-3 have generalized 1-type Gauss map. Second, we classify conical surfaces with generalized 1-type Gauss map in L-3. After then, nonplanar tangent developable surfaces in the Minkowski 3-space L-3 with generalized 1-type Gauss map are open pieces of a Euclidean plane or a Minkowski plane. Finally, we show that a null scroll in the Minkowski 3-space L-3 has generalized 1-type Gauss map if and only if it is either an open piece of a Minkowski plane or a B-scroll.