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Bounded geodesics in rank-1 locally symmetric spaces

Published online by Cambridge University Press:  14 October 2010

C. S. Aravinda  and
Enrico Leuzinger
C. S. Aravinda
Affiliation:
School of Mathematics, TIFR, Homi Bhabha Road, Bombay-400005, India
Enrico Leuzinger
Affiliation:
Mathematisches Institut, Universitat Zurich, Winterthurerstrasse 190, CH-8057, Zurich, Switzerland
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Abstract

Let M be a rank 1 locally symmetric space of finite Riemannian volume. It is proved that the set of unit vectors on a non-constant C1 curve in the unit tangent sphere at a point p ∈ M for which the corresponding geodesic is bounded (relatively compact) in M, is a set of Hausdorff dimension 1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 5 , October 1995 , pp. 813 - 820
Copyright
Copyright © Cambridge University Press 1995

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References

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