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Proceedings of the American Mathematical Society

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Bohr almost periodic maps
into $K(\pi ,1)$ spaces

Author: Sol Schwartzman
Journal: Proc. Amer. Math. Soc. 125 (1997), 427-431
MSC (1991): Primary 43A60, 58F22
MathSciNet review: 1350962
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Abstract: Let $X$ be a locally finite simplicial complex of finite topological dimension. Assume further that $X$ is a $K(\pi ,1)$ space where $\pi $ is a group whose only abelian subgroups are infinite cyclic. We prove that a Bohr almost periodic map of the real line into $X$ is uniformly homotopic to a periodic map. As a consequence we show that a Bohr almost periodic geodesic on a compact Riemannian manifold of everywhere negative curvature is necessarily periodic.

References [Enhancements On Off] (What's this?)

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  • 2. Manfredo do Carmo, Riemannian geometry, Birkhäuser, Boston, MA, 1992. MR 92i:53001
  • 3. W. Fenchel and B. Jessen, Über fastperiodischen Bewegungen in ebenen Bereichen und auf Flächen, Danske Vid. Selsk., Math.-Fys. Medd. 13 (1935), no. 6, 1-28.
  • 4. Ya. B. Pesin, Geodesic flows with hyperbolic behavior of the trajectories and objects connected with them, Russian Math. Surveys 36 (1981), no. 4, 1-59. MR 82j:58095

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Additional Information

Sol Schwartzman
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

Received by editor(s): May 22, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society

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