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arXiv · 0706.0332

Positive Complex Sectional Curvature, Ricci Flow and the Differential Sphere Theorem

Lei Ni·Jon Wolfson
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Abstract

The paper provides a different proof of the result of Brendle-Schoen on the differential sphere theorem. It is shown directly that the invariant cone of curvature operators with positive (or non-negative) complex sectional curvature is preserved by the Ricci flow. This implies, by a result of Böhm-Wilking, that the normalized Ricci flow deforms such a metric to a metric of constant positive curvature. Using earlier work of Yau and Zheng it can be shown that a metric with strictly (pointwise) 1/4-pinched sectional curvature has positive complex sectional curvature. This gives a direct proof of Brendle-Schoen's recent differential sphere theorem, bypassing any discussion of positive isotropic curvature.

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Lei Ni, Jon Wolfson. 2007-06-03. Positive Complex Sectional Curvature, Ricci Flow and the Differential Sphere Theorem. https://arxiv.org/abs/0706.0332

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