Global behavior of curves in a space of positive curvature
HTML articles powered by AMS MathViewer
- by B. V. Dekster
- Proc. Amer. Math. Soc. 85 (1982), 419-426
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656116-7
- PDF | 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.References
- Jeff Cheeger and Detlef Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443. MR 309010, DOI 10.2307/1970819
- B. V. Dekster, Estimates of the length of a curve, J. Differential Geometry 12 (1977), no. 1, 101–117. MR 470906
- 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
- B. V. Dekster and I. Kupka, Asymptotics of curvature in a space of positive curvature, J. Differential Geometry 15 (1980), no. 4, 553–568 (1981). MR 628344
- Detlef Gromoll and Wolfgang Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90. MR 247590, DOI 10.2307/1970682
- Ju. G. Rešetnjak, Bound for the length of a rectifiable curve in $n$-dimensional space. , Sibirsk. Mat. Ž. 2 (1961), 261–265 (Russian). MR 0125939
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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