On the regularity of oricyclic coordinates

E. V. Shikin

M. V. Lomonosov Moscow State University

Abstract: Suppose there is defined in the plane a complete metric $W^-$, whose curvature $K$ satisfies the inequality $-k_2^2\le K\le -k_1^2$ ($k_1$ and $k_2$ are positive constants) and some regularity hypothesis. Then in the entire domain of definition of the metric $W^-$ one can construct regular oricyclic coordinates $(x,y)$, in which the line element has the form $ds^2=dx^2+B2(x,y)\cdot dy^2$.

Received: 21.11.1974

 English version: Mathematical Notes, 1975, 17:3, 277–282

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