Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • 1. Harald Bohr, Collected Mathematical Works. Vol. I. Dirichlet series. The Riemann zeta-function. Vol. II. Almost periodic functions. Vol. III. Almost periodic functions (continued). Linear congruences. Diophantine approximations. Function theory. Addition of convex curves. Other papers. Encyclopædia article. Supplements, Dansk Matematisk Forening, København, 1952 (Italian). MR 0057790
  • 2. Manfredo Perdigão do Carmo, Riemannian geometry, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 1992. Translated from the second Portuguese edition by Francis Flaherty. MR 1138207
  • 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. Ja. B. Pesin, Geodesic flows with hyperbolic behavior of trajectories and objects connected with them, Uspekhi Mat. Nauk 36 (1981), no. 4(220), 3–51, 247 (Russian). MR 629682

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A60, 58F22

Retrieve articles in all journals with MSC (1991): 43A60, 58F22


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03598-3
Received by editor(s): May 22, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society