Global behavior of curves in a space of positive curvature
Author:
B. V. Dekster
Journal:
Proc. Amer. Math. Soc. 85 (1982), 419-426
MSC:
Primary 53C40; Secondary 53C20
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656116-7
MathSciNet review:
656116
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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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- B. V. Dekster, Upper estimates of the length of a curve in a Riemannian manifold with boundary, J. Differential Geometry 14 (1979), no. 2, 149–166. MR 587544
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Article copyright:
© Copyright 1982
American Mathematical Society
