Two-Dimensional Nonisotropic Surfaces with Flat Normal Connection and a Nondegenerate Grassmann Image of Constant Curvature in the Minkowski Space

We find possible values of curvature of the Grassmann manifold along the planes tangential to the Grassmann image of a two-dimensional nonisotropic surface with flat normal connection in the fourdimensional Minkowski space. It is shown that if the surface with flat normal connection is time-like, then the analyzed curvature may take values from the set [0, 1]. However, if the surface with flat normal connection is space-like, then this curvature may take values from the set (−∞,−1] in the case of a space-like Grassmann image or the values from the set [0, ∞) in the case of a time-like Grassmann image. The existence of two-dimensional nonisotropic surfaces with flat normal connection and constant curvature of their Grassmann image is proved for all values of curvature from the obtained sets.