Open manifolds of nonnegative curvature

DOI10.1007/BF01095906zbMath0729.53041OpenAlexW2038986802MaRDI QIDQ806067

V. A. Toponogov, Valery Borisovich Marenich

Publication date: 1991

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01095906

zbMATH Keywords

homotopy typeRicci curvatureKähler manifoldsholonomy groupnon-negative sectional curvaturefiniteness theoremsconjecture of Cheeger and Gromoll

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Global Riemannian geometry, including pinching (53C20) Issues of holonomy in differential geometry (53C29) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Cites Work

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• An improved Toponogov comparison theorem for nonnegatively curved manifolds
• An elementary proof of the Cheeger-Gromoll splitting theorem
• Gap theorems for noncompact Riemannian manifolds
• P-convex Riemannian manifolds
• On complete Kähler manifolds with fast curvature decay
• Some complete manifolds with non-negative curvature operator
• Metric of non-negative sectional curvature on the tangent bundle of the two-dimensional sphere
• Examples of manifolds of positive Ricci curvature
• A splitting theorem for open nonnegatively curved manifolds
• Nonnegatively curved manifolds with souls of codimension 2
• Bounding homotopy types by geometry
• Handlebodies and p-convexity
• On the structure of locally convex filtrations on complete manifolds
• Curvature at infinity of open nonnegatively curved manifolds
• Busemann functions and total curvature
• Convex sets in a manifold of nonnegative curvature
• Geodesic spheres as generators of the homotopy groups of O,BO
• The classification of simply connected manifolds of positive scalar curvature
• Positive Ricci curvature on fibre bundles
• Curvature, diameter and Betti numbers
• Convex functions on complete noncompact manifolds: Topological structure
• Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres
• On three-dimensional Riemannian spaces with curvature bounded above
• A generalization of the Cheeger-Gromoll splitting theorem
• Some examples of manifolds of nonnegative curvature
• Complete open manifolds of nonnegative curvature
• The structure of open manifolds of nonnegative curvature. II
• The fundamental equations of a submersion
• On complete open manifolds of positive curvature
• The splitting theorem for manifolds of nonnegative Ricci curvature
• On the structure of complete manifolds of nonnegative curvature
• An extension of Rauch's metric comparison theorem and some applications
• On Complete Manifolds With Nonnegative Ricci Curvature
• Lower curvature bounds, Toponogov's theorem, and bounded topology
• Locally Geodesically Quasiconvex Functions on Complete Riemannian Manifolds
• Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups
• Lower curvature bounds, Toponogov's theorem, and bounded topology. II
• Convex functions on complete noncompact manifolds : differentiable structure
• CONVEX SETS IN RIEMANNIAN SPACES OF NON-NEGATIVE CURVATURE
• Metrics of Negative Curvature on Vector Bundles
• Finiteness Theorems for Riemannian Manifolds