In 1+1 Minkowski space the distance between two points is given by$$ (x_1 -x_2)^2 -(t_1 - t_2)^2.$$

This is different from the Euclidean distance. But is it possible to come up with a 2D surface embedded in 3D Euclidean space such that the geodesic distance between two points on the surface is like that in Minkowski space?