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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the variety of manifolds without conjugate points


Author: Robert Gulliver
Journal: Trans. Amer. Math. Soc. 210 (1975), 185-201
MSC: Primary 53C20; Secondary 58F15
DOI: https://doi.org/10.1090/S0002-9947-1975-0383294-0
MathSciNet review: 0383294
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Abstract: The longest geodesic segment in a convex ball of a riemannian manifold, where the convexity is ensured by an upper bound on sectional curvatures, is the diameter. This and related results are demonstrated and applied to show that there exist manifolds with sectional curvatures of both signs but with-out conjugate points.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0383294-0
Keywords: Conjugate points, riemannian manifold, length of geodesic segments, Anosov geodesic flow
Article copyright: © Copyright 1975 American Mathematical Society