Some class of surfaces of negative curvature with singularities on lines (Q1065364)

The author constructs a surface in Euclidean space \(R^ 3\) with properties: it is of class \(C^ 1\); it is of class \(C^ 2\) everywhere except for some line \({\mathcal L}\), the Gauss curvature is negative and continuous everywhere, including \({\mathcal L}\). It is shown that such surfaces can be constructed in a neighborhood of any smooth surface of negative Gauss curvature.