Sharafutdinov'S Retraction

(Riemannian Geometry)


Riemannian Geometry
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What is Sharafutdinov's retraction?

In mathematics, Sharafutdinov's retraction is a construction that gives a retraction of an open non-negatively curved Riemannian manifold onto its soul. It was first used by to show that any two souls of a complete Riemannian manifold with non-negative sectional curvature are isometric. Perelman later showed that in this setting, Sharafutdinov's retraction is in fact a submersion, thereby essentially settling the soul conjecture. For open non-negatively curved Alexandrov space, Perelman also showed that there exists a Sharafutdinov retraction from the entire space to the soul. However it is not yet known whether this retraction is submetry or not.

Technology Types

riemannian geometry


Ретракция Шарафутдинова (ru)

Tech Info

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 — Date merged: 11/6/2021, 1:33:02 PM
 — Date scraped: 5/20/2021, 6:15:04 PM