This article is cited in 3 papers

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

È. R. Rozendorn


Abstract: 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.
Bibliography: 12 titles.

UDC: 513.736.35

MSC: 53C40

Received: 07.07.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 18:1, 83–92

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