Global behavior of curves in a space of positive curvature

Dekster, B. V.

doi:10.1090/S0002-9939-1982-0656116-7

Global behavior of curves in a space of positive curvature
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Proc. Amer. Math. Soc. 85 (1982), 419-426 Request permission

Abstract:

It is well known that any geodesic in a complete noncompact space of positive curvature goes to infinity. In this paper, we prove that this is true for more general curves and estimate how fast they go to infinity in terms of their curvature and curvature of the space.

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