Abstract:
In this paper it is shown that in any C1C1-neighborhood of the standard metric H0H0 on S2S2, there exists a subset consisting of convex metrics, which is open in the C2C2-topology, and all of whose closed nonselfintersecting geodesics are hyperbolic.
Bibliography: 13 titles.
Citation:
A. I. Gryuntal', “The existence of convex spherical metrics, all closed nonselfintersecting geodesics of which are hyperbolic”, Math. USSR-Izv., 14:1 (1980), 1–16
\Bibitem{Gry79}
\by A.~I.~Gryuntal'
\paper The existence of convex spherical metrics, all closed nonselfintersecting geodesics of which are hyperbolic
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 1
\pages 1--16
\mathnet{http://mi.mathnet.ru/eng/im1574}
\crossref{https://doi.org/10.1070/IM1980v014n01ABEH001057}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=525939}
\zmath{https://zbmath.org/?q=an:0433.53032|0403.53021}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980KM22000001}
Linking options:
https://www.mathnet.ru/eng/im1574
https://doi.org/10.1070/IM1980v014n01ABEH001057
https://www.mathnet.ru/eng/im/v43/i1/p3
This publication is cited in the following 5 articles:
Gonzalo Contreras, Marco Mazzucchelli, “Proof of the C2-stability conjecture for geodesic flows of closed surfaces”, Duke Math. J., 173:2 (2024)
Yi-ming Long, “Index iteration theory for symplectic paths and multiple periodic solution orbits”, Front Math China, 1:2 (2006), 178
Jean-Jacques Sansuc, Vadim Tkachenko, Algebraic and Geometric Methods in Mathematical Physics, 1996, 371
I. A. Taimanov, “Closed extremals on two-dimensional manifolds”, Russian Math. Surveys, 47:2 (1992), 163–211
M.S Berger, E Bombieri, “On Poincaré's isoperimetric problem for simple closed geodesics”, Journal of Functional Analysis, 42:3 (1981), 274
Citation in format AMSBIB
Contact us: