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

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dc.creatorNi, Lei
dc.creatorWolfson, Jon
dc.date2007-06-03
dc.date.accessioned2026-07-07T08:03:59Z
dc.date.available2026-07-07T08:03:59Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/0706.0332
dc.identifierhttp://arxiv.org/abs/0706.0332
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129786
dc.subjectDifferential Geometry
dc.subject53C21, 58J35
dc.titlePositive Complex Sectional Curvature, Ricci Flow and the Differential Sphere Theorem
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