Asian Journal of Mathematics

Volume 13 (2009)

Number 2

Four-manifolds with 1/4-pinched Flag Curvatures

Pages: 251 – 270

DOI: https://dx.doi.org/10.4310/AJM.2009.v13.n2.a5

Authors

Ben Andrews (Mathematical Sciences Institute, Australia National University, Canberra, Australia; and Mathematical Sciences Center, Tsinghua University, Beijing, China)

Huy Nguyen

Abstract

The Ricci flow on a compact four-manifold preserves the condition of pointwise 1/4- pinching of flag curvatures. Any compact Riemannian four-manifold with 1/4-pinched flag curvatures is either isometric to $\Bbb C\Bbb P^{2}$ or diffeomorphic to a space-form.

Keywords

Ricci flow, Sphere theorem

2010 Mathematics Subject Classification

Primary 53C20, 53C44. Secondary 35K55, 53C21, 58J35.

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Published 1 January 2009