The exactness of smoothness theorems for surfaces with a given smooth negative curvature (Q1358358)

The author suggests a method for constructing surfaces of class \(C^{n+1}\), \(n \geq 1\), which have negative Gaussian curvature of class \(C^n\). Here \(C^n\)-smoothness of the curvature \(K\) is understood in the sense of intrinsic geometry; namely, \(K\) is regarded as a function of semigeodesic coordinates \((u,v)\). Using this method the author proves the exactness of the earlier proved smoothness theorems for surfaces with given smooth negative curvature.