Asian Journal of Mathematics

Four-manifolds with 1/4-pinched Flag Curvatures

Ben Andrews and Huy Nguyen

Full-text: Open access

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.

Article information

Source
Asian J. Math., Volume 13, Number 2 (2009), 251-270.

Dates
First available in Project Euclid: 27 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1256650871

Mathematical Reviews number (MathSciNet)
MR2559110

Zentralblatt MATH identifier
1187.53066

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 35K55: Nonlinear parabolic equations 58J35: Heat and other parabolic equation methods 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Keywords
Ricci flow Sphere theorem

Citation

Andrews, Ben; Nguyen, Huy. Four-manifolds with 1/4-pinched Flag Curvatures. Asian J. Math. 13 (2009), no. 2, 251--270. https://projecteuclid.org/euclid.ajm/1256650871


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