The nonembeddability of complete $q$-metrics of negative curvature in a class of weakly nonregular surfaces

In this paper it is proved that a regular complete two-dimensional Riemainnian metric $ds^2$, having curvature $K<0$ subject to the condition $\sup|\frac\partial{\partial s}(|K|^{1/2})|<+\infty$, cannot be embedded in $R^3$ in the class of smooth surfaces regular except at a number of isolated points. The result is extended to metrics with singular points.
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