References
[A]A. Avez, Variétés riemanniennes sans points focaux. C.R.A.S. A-B 270 (1970), A 188–191.
[B]I. Babenko, Asymptotic volume of tori and geometry of convex bodies, Mat. Zametki 44:2 (1988), 177–188.
[Ba1]V. Bangert, Minimal geodesics, Erg. Theory and Dyn. Syst. 10 (1990), 263–286.
[Ba2]V. Bangert, Geodesic rays, Busemann functions and monotone twist maps. Calc. Var. 2 (1994), 49–63.
[Bu1]D. Burago, Periodic metrics, Advances in Soviet Math. 9, New York (1992), 205–210.
[Bu2]D. Burago, Periodic Metrics, In “Seminar on Dynamical Systems”, Progress in Nonlinear Differential Equations (H. Brezis, ed.) 12, 90–96, Birkhauser, 1994.
[BurZ]Yu. Burago, V. Zalgaller, Geometric Inequalities. Springer-Verlag 1988.
[Bus]H. Busemann, The Geometry of Geodesics, Acad. Press, New York, 1955.
[C]C. Croke, Volumes of balls in manifolds without conjugate points, Int. J. Math. 3:4 (1992), 455–467.
[CF]C. Croke, A. Fathi, An inequality between energy and intersections, Bull. London Math. Soc. 22 (1990), 489–494.
[CK]C. Croke, B. Kleiner, On tori without conjugate points, Preprint.
[G]L. Green, A theorem of E. Hopf, Mich. Math. J. 5 (1958), 31–34.
[Gr]M. Gromov, Dimension, non-linear spectra and width, Springer Lecture Notes in Mathematics 1317 (1988), 132–184.
[H]J. Heber, Personal communication.
[HeM]G. Hedlund, M. Morse, Manifolds without conjugate points, Trans. Amer. Math. Soc. 51 (1942), 362–386.
[Ho]E. Hopp, Closed Surfaces Without Conjugate Points, Proc. Nat. Acad. of Sci. 34, 1948.
[Kn]A. Knauf, Closed orbits and converse KAM Theory, Nonlinearity 3 (1990), 961–973.
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The first author was supported by the “Deutsche Forschungsgemeinschaft” fellowship and enjoyed the hospitality of the University of Freiburg.
Both authors can be reached by e-mail at burago@ibs.spb.su, burago@lomi.spb.su or sliss@iian.spb.su; the first and last name of the addressee should be explicitly stated.
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Burago, D., Ivanov, S. Riemannian tori without conjugate points are flat. Geometric and Functional Analysis 4, 259–269 (1994). https://doi.org/10.1007/BF01896241
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DOI: https://doi.org/10.1007/BF01896241