The metric projection onto the soul

DOI10.1090/S0002-9947-99-02237-0zbMath0963.53017MaRDI QIDQ4700120

Gerard Walschap, Luis Guijarro

Publication date: 1 November 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

convexitytotally geodesic submanifoldnonnegative curvaturesoulSharafutdinov retractionpseudosoul

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (14)

Conditions for nonnegative curvature on vector bundles and sphere bundles. ⋮ Obstructions to nonnegative curvature and rational homotopy theory ⋮ Strongly nonnegative curvature ⋮ Metrics with nonnegative curvature on \({S^2 \times \mathbb{R}^4}\) ⋮ Riemannian submersions from compact four manifolds ⋮ Rigidity for odd-dimensional souls ⋮ A characterization of codimension one collapse under bounded curvature and diameter ⋮ Flats and submersions in non-negative curvature ⋮ Finiteness theorems for submersions and souls ⋮ The dual foliation in open manifolds with nonnegative sectional curvature ⋮ Geometrical and analytical properties of Chebyshev sets in Riemannian manifolds ⋮ Nonnegatively curved Alexandrov spaces with souls of codimension two ⋮ Topology of codimension-one foliations of nonnegative curvature ⋮ Index theory and deformations of open nonnegatively curved manifolds

Cites Work

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• Space of souls in a complete open manifold of nonnegative curvature
• Gap theorems for noncompact Riemannian manifolds
• Submetries of space forms of nonnegative curvature
• A splitting theorem for open nonnegatively curved manifolds
• Nonnegatively curved manifolds with souls of codimension 2
• Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature
• The regular focal locus
• \(\Sigma\)-flat manifolds and Riemannian submersions
• Proof of the soul conjecture of Cheeger and Gromoll
• Soul-preserving submersions
• The low-dimensional metric foliations of Euclidean spheres
• Some examples of manifolds of nonnegative curvature
• The fundamental equations of a submersion
• On the structure of complete manifolds of nonnegative curvature
• The Soul at Infinity in Dimension 4
• Volumes of Small Balls on Open Manifolds: Lower Bounds and Examples
• Vector Bundles with No Soul
• Rigidity in non-negative curvature1
• Improving the metric in an open manifold with nonnegative curvature
• The Conjugate Locus of a Riemannian Manifold

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