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
isometric.[1] Perelman later showed that in this setting, Sharafutdinov's retraction is in fact a submersion, thereby essentially settling the soul conjecture.[2]
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.
References
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