Geodesic flow in certain manifolds without conjugate points
Author:
Patrick Eberlein
Journal:
Trans. Amer. Math. Soc. 167 (1972), 151170
MSC:
Primary 58E10; Secondary 53C20
MathSciNet review:
0295387
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Abstract: A complete simply connected Riemannian manifold H without conjugate points satisfies the uniform Visibility axiom if the angle subtended at a point p by any geodesic of H tends uniformly to zero as the distance from p to tends uniformly to infinity. A complete manifold M is a uniform Visibility manifold if it has no conjugate points and if the simply connected covering H satisfies the uniform Visibility axiom. We derive criteria for the existence of uniform Visibility manifolds. Let M be a uniform Visibility manifold, SM the unit tangent bundle of M and the geodesic flow on SM. We prove that if every point of SM is nonwandering with respect to then is topologically transitive on SM. We also prove that if is a normal covering of M then is topologically transitive on if is topologically transitive on SM.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197202953874
PII:
S 00029947(1972)02953874
Keywords:
Geodesic flow,
conjugate points,
nonwandering points,
topological transitivity,
uniform Visibility
Article copyright:
© Copyright 1972
American Mathematical Society
