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Chapitre D'ouvrage Année : 2016

The Differentiable Sphere Theorem (After S. Brendle and R. Schoen)

Gérard Besson

Résumé

In these notes we describe a major result obtained recently using the Ricci flow technique in the context of positive curvature. It is due to S. Brendle and R. Schoen and states that a strictly 1/4-pinched closed manifold carries a metric of constant (positive) sectional curvature. It relies on a technique developed by C. Böhm and B. Wilking who obtained the same conclusion assuming that the manifold has positive curvature operator. The maximum principle applied to the Ricci flow equation leads to studying an ordinary differential equation on the space of curvature operators.
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Dates et versions

hal-01621636 , version 1 (23-10-2017)

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  • HAL Id : hal-01621636 , version 1

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Gérard Besson. The Differentiable Sphere Theorem (After S. Brendle and R. Schoen). Riccardo Benedetti; Carlo Mantegazza. Ricci Flow and Geometric Applications , 2166, Springer, pp.1-19, 2016, Lecture Notes in Mathematics book series (LNM), 978-3-319-42350-0. ⟨hal-01621636⟩
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