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- 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. (en)
- Ретракция Шарафутдинова — конструкция, позволяющая построить ретракцию риманова многообразия по выпуклой функции на нём. Впервые использована в 1979 году в доказательстве того, что любые две души в многообразии с неотрицательной секционной кривизной изометричны. (ru)
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- Ретракция Шарафутдинова — конструкция, позволяющая построить ретракцию риманова многообразия по выпуклой функции на нём. Впервые использована в 1979 году в доказательстве того, что любые две души в многообразии с неотрицательной секционной кривизной изометричны. (ru)
- 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. (en)
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- Sharafutdinov's retraction (en)
- Ретракция Шарафутдинова (ru)
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