Two-dimensional nonisotropic surfaces with flat normal connection and a nondegenerate Grassmann image of constant curvature in the Minkowski space - Stegantseva, P.; Grechneva, M. (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 514.764 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 four-dimensional 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 (-∞,-1] in the case of a space-like Grassmann image or the values from [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.