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A characterization of flat metrics on tori by ergodicity

Published online by Cambridge University Press:  19 September 2008

Nobuhiro Innami
Nobuhiro Innami
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima, 730, Japan and Department of Mathematics, Nagoya Institute of Technology, Nagoya, 466, Japan
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Abstract

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The Riemannian flat metrics on tori T2 are characterized by a weakly ergodic property of the geodesic flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 2 , June 1987 , pp. 197 - 201
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Ballmann, W. & Brin, M.. On the ergodicity of geodesic flows. Ergod. Th. & Dynam. Syst. 2 (1982), 311–315.Google Scholar
[2]Bangert, V.. Mather sets for twist maps and geodesies on tori. Preprint.Google Scholar
[3]Bliss, G. A.. The geodesics on an anchor ring. Ann. of Math. 4 (1903), 1–20.CrossRefGoogle Scholar
[4]Busemann, H.. The Geometry of Geodesics. Academic Press: New York, 1955.Google Scholar
[5]Busemann, H.. Recent Synthetic Differential Geometry. Springer-Verlag: Berlin-Heidelberg-New York, 1970.Google Scholar
[6]Busemann, H. & Pedersen, F. P.. Tori with one-parameter groups of motions. Math. Scand. 3 (1955), 209–220.CrossRefGoogle Scholar
[7]Green, L. W.. Surfaces without conjugate points. Trans. Amer. Math. Soc. 76 (1954), 529–546.CrossRefGoogle Scholar
[8]Innami, N.. On tori having poles. Invent. Math., 84 (1986), 437–443.Google Scholar
[9]Innami, N.. Families of geodesies which distinguish flat tori. To appear in Math. J. Okayama Univ. (1987).Google Scholar
[10]Kimball, B. F.. Geodesies on a toroid. Amer. J. Math. 52 (1930), 29–52.Google Scholar
[11]Klingenberg, W.. Riemannian Geometry. Walter de Gruyter: Berlin-New York, 1982.Google Scholar
[12]Wolf, J. A.. Homogeneity and bounded isometries in manifolds of negative curvature. Illinois J. Math. 8 (1964), 14–18.Google Scholar