Two-dimensional nonisotropic surfaces with flat normal connection and a nondegenerate Grassmann image of constant curvature in the Minkowski space (Q6633996)

The paper under review addresses two questions about the Grassmann image of \(2\)-dimensional surfaces in Minkowski \(4\)-space with flat normal connection:\N\begin{itemize}\N\item What values can be taken by the curvature of the Grassmann image?\N\item For what values of \(k\), surfaces with flat normal connection and a Grassmann image of constant curvature \(k\) may exist?\N\end{itemize}\N\NFor the first question, it is shown that if the surface is time-like, then the curvature of the Grassmann image may take values from the set \([0, 1]\); if it is space-like, then this curvature may take values from the set \((-1, -1]\) in the case of a space-like Grassmann image or values from the set \([0, 1)\) in the case of a time-like Grassmann image.\N\NAs for the second question, the existence of two-dimensional nonisotropic surfaces with flat normal connection and constant curvature of their Grassmann image is proved for all values \(k\) belonging to the above intervals.