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Three-dimensional open Riemannian space of nonnegative curvature. (English) Zbl 0405.53026


MSC:

53C20 Global Riemannian geometry, including pinching

Citations:

Zbl 0364.53016
Full Text: DOI

References:

[1] S. Cohn-Vossen, ?Kurzeste Wege und Totalkrummung auf Flachen,? Compositio Math.,2, 69?133 (1935).
[2] J. Cheeger and D. Gromoll, ?On the structure of complete manifolds of nonnegative curvature,? Ann. Math.,96, No. 3, 413?443 (1972). · Zbl 0246.53049 · doi:10.2307/1970819
[3] V. A. Sharafutdinov, ?Complete open manifolds of nonnegative curvature,? Sib. Math. Zh., 15, No. 1, 177?191 (1974).
[4] V. A. Sharafutdinov, ?Complete open manifolds of nonnegative curvature,? Dissertion, Novosibirsk State Univ. (1973).
[5] W. A. Poor, ?Some results on nonnegatively curved manifolds,? J. Diff. Geom.,9, No. 4, 583?600 (1974). · Zbl 0292.53037 · doi:10.4310/jdg/1214432557
[6] R. Walter, ?Some analytical properties of geodesically convex sets,? to be published.
[7] R. Walter, ?A generalized Allendorffer-Weil formula and an inequality of the Cohn-Vossen type,? J. Diff. Geom.,10, No. 2, 167?180 (1975). · Zbl 0308.53042 · doi:10.4310/jdg/1214432786
[8] R. Walter, ?On the metric projection onto convex sets in Riemannian spaces,? Arch. Math.,25, 91?98 (1974). · Zbl 0311.53054 · doi:10.1007/BF01238646
[9] S. S. Chern, ?On the curvature and characteristic classes of a Riemannian manifold,? Abh. Math. Sem. Univ. Hamburg,20, No. 1, 117?126 (1955). · Zbl 0066.17003 · doi:10.1007/BF02960745
[10] R. Geroch, ?Positive sectional curvature does not imply positive Gauss-Bonnet integrand,? Proc. Am. Math. Soc.,54, 267?270 (1976). · Zbl 0325.53042 · doi:10.1090/S0002-9939-1976-0390961-8
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