Generalized Null 2-Type Surfaces in Minkowski 3-Space

Abstract

For the mean curvature vector field H and the Laplace operator of a submanifold in the Minkowski space, a submanifold satisfying the condition H = fH +gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper, we study flat surfaces in the Minkowski 3-space L 3 and classify generalized null 2-type flat surfaces. In addition, we show that the only generalized null 2-type null scroll in L 3 is a B-scroll.