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Note on uniform visibility manifolds

Published online by Cambridge University Press:  24 October 2008

Donal Hurley
Donal Hurley
Affiliation:
Department of Mathematics, University College, Cork, Ireland
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Extract

The axiom of uniform visibility on simply connected manifolds was introduced in [8] by Eberlein and O'Neill. Using the axiom, they were able to extend to a class of simply connected manifolds of non-positive sectional curvature many results which were known to be true for the case of strictly negative curvature. The axiom proved very useful in obtaining results about the geodesic flow on manifolds of non-positive sectional curvature [3], [4].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 73 - 80
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Ballmann, W.. Axial isometries of manifolds of non-positive curvature. Math. Ann. 259 (1982), 131–144.CrossRefGoogle Scholar
[2]Druetta, M. J.. Clifford translations in manifolds without focal points. Geom. Dedicata 14 (1983), 95–103.CrossRefGoogle Scholar
[3]Eberlein, P.. Geodesic flows on negatively curved manifolds I. Ann. of Math. 95 (1972), 492–510.CrossRefGoogle Scholar
[4]Eberlein, P.. Geodesic flows on negatively curved manifolds II. Trans. Amer. Math. Soc. 178 (1973), 57–82.CrossRefGoogle Scholar
[5]Eberlein, P.. When is a geodesic flow of Anosov type I? J. Differential Geom. 8 (1973), 437–463.Google Scholar
[6]Eberlein, P.. When is a geodesic flow of Anosov type II? J. Differential Geom. 8 (1973), 565–577.Google Scholar
[7]Eberlein, P.. Geodesic flow in certain manifolds without conjugate points. Trans. Amer. Math. Soc. 167 (1972), 151–170.CrossRefGoogle Scholar
[8]Eberlein, P. and O'Neill, B.. Visibility manifolds. Pacific J. Math. 46 (1973), 45–109.CrossRefGoogle Scholar
[9]Eschenburg, J.-H. and O'Sullivan, J. J.. Growth of Jacobi fields and divergence of geodesies. Math. Z. 150 (1976), 221–237.CrossRefGoogle Scholar
[10]O'Sullivan, J.J.. Riemannian manifolds without focal points. J. Differential Geom. 11 (1976), 321–333.CrossRefGoogle Scholar
[11]Pesin, Ja. B.. Geodesic flows on closed Riemannian manifolds without focal points. Math. U.S.S.R. Izvesitja 11 (1977), 1195–1228.Google Scholar