caa a22 4500 477118291 CHVBK 20180405111628.0 cr unu---uuuuu 170330e19960101xx s 000 0 eng 10.1007/BF02259624 doi (NATIONALLICENCE)springer-10.1007/BF02259624 Polterovich I. Dept. of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia aut On a characterization of flat metrics on 2-torus [Elektronische Daten] [I. Polterovich] A well-known theorem by E. Hopf states that if a Riemannian 2-torus has no conjugate points, then its Gaussian curvature vanishes identically. This result is a generalization of a theorem by M. Morse and G. Hedlund who have proved that a 2-torus without focal points is flat. In the present paper it is shown that under some additional assumptions a 2-torus is flat if there are no focal points just on a single geodesic. Plenum Publishing Corporation, 1996 Geodesic flow nationallicence invariant torus nationallicence Jacobi field nationallicence diffeomorphism of a circle nationallicence Journal of Dynamical and Control Systems Kluwer Academic Publishers-Plenum Publishers 2/1(1996-01-01), 89-101 1079-2724 2:1<89 1996 2 10883 https://doi.org/10.1007/BF02259624 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02259624 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Polterovich I. Dept. of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Kluwer Academic Publishers-Plenum Publishers 2/1(1996-01-01), 89-101 1079-2724 2:1<89 1996 2 10883 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer