On the existence of a minimal time-like surface of the Minkowski space with constant curvature of its Grassmann image

We investigate the curvature of the Grassmann manifold along planes tangent to the Grassmann image of two-dimensional time-like minimal surfaces in four-dimensional Minkowski space. We establish the existence of two-dimensional time-like minimal surfaces whose Grassmann images exhibit constant curvature K=1. Furthermore, we demonstrate that no time-like minimal surfaces exist with a non-degenerate Grassmann image of constant curvature K≠1.