CONFORMAL TRANSFORMATIONS OF SURFACES IN MINKOWSKI SPACE WHICH PRESERVE THE GRASSMANN IMAGE

摘要

In the present paper we study two-dimensional surfaces in an n-dimensional Minkowski space Mn and their conformal G-transformations. For surfaces F2 and F2 in Mn, a map Φ:F2 → F2 is called a G-transforrnation if the plane tangent to F2 at p ∈ F2 is parallel to the plane tangent to F2 at Φ(p) ∈ F2. In other words, a G-transformation is a transformation which pointwise preserves the Grassmann image of surface. A G-transformation Φ : F2 → F2 is said to be conformal if the first fundamental form of F2 at p ∈ F2 is proportional to the first fundamental form of F2 at Φ(p) ∈ F2. The simplest examples of conformal G-transformations are translations and homothetic transformations of the ambient space Mn.