On the variety of manifolds without conjugate points

Gulliver, Robert

doi:10.1090/S0002-9947-1975-0383294-0

On the variety of manifolds without conjugate points
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Trans. Amer. Math. Soc. 210 (1975), 185-201 Request permission

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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