This article is cited in 5 papers

The existence of convex spherical metrics, all closed nonselfintersecting geodesics of which are hyperbolic

A. I. Gryuntal'


Abstract: In this paper it is shown that in any $C^1$-neighborhood of the standard metric $H_0$ on $S^2$, there exists a subset consisting of convex metrics, which is open in the $C^2$-topology, and all of whose closed nonselfintersecting geodesics are hyperbolic.
Bibliography: 13 titles.

UDC: 517.9

MSC: Primary 53C20, 58C99; Secondary 34C40

Received: 13.06.1978

 English version: Mathematics of the USSR-Izvestiya, 1980, 14:1, 1–16

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