References
W. Ballmann, M. Gromov andV. Schroeder,Manifolds of nonpositive curvature, Birkhäuser, Basel-Boston 1985.
J. Cheeger andD. Ebin,Comparison theorems in Riemannian geometry, North Holland, Amsterdam, 1975.
J. Cheeger andD. Gromoll,On the structure of complete manifolds of nonnegative curvature, Annals of Math.96 (1972), 413–443.
J. Eschenburg andV. Schroeder,Riemannian manifolds with flat ends to appear in Math. Zeitschrift.
M. Gromov,Curvature, diameter and Betti numbers, Comm. Math. Helv.56 (1981) 179–195.
R. Greene andH. Wu,Gap theorems for noncompact Riemannian manifolds, Duke Math. J.49 (1982), 731–756.
R. Sacksteder,On hypersurfaces with nonnegative sectional curvature, American J. of Math.82 (1960) 609–630.
V. A. Sharafudtinov,Convex sets in a manifold of nonnegative curvature, Math. Notes of the Ac. of Sc. of the USSR (Mat. Zametki)26 (1979) 556–560.
V. Schroeder andM. Strake,Local rigidity of symmetric spaces of nonpositive curvature, preprint Universität Münster.
V. Schroeder andW. Ziller,Local rigidity of symmetric spaces, preprint Univ. of Pennsylvania 1987.
J. P. Sha andD. G. Yang,Examples of manifolds of positive Ricci curvature, preprint Univ. of Pennsylvania 1987.
W. Thurston,The geometry and topology of 3-manifolds, Lecture Notes, Princeton University 1978.
J. W. Yim,Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature, preprint Univ. of Pennsylvania 1987.
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Schroeder, V., Strake, M. Rigidity of convex domains in manifolds with nonnegative Ricci and sectional curvature. Commentarii Mathematici Helvetici 64, 173–186 (1989). https://doi.org/10.1007/BF02564668
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DOI: https://doi.org/10.1007/BF02564668