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Compact Riemannian manifolds with positive curvature operators. (English) Zbl 0589.53048
A compact simply connected Riemannian n-manifold (n\(\geq 4)\) with positive curvature operators (on \(\Lambda^ 2TM)\) is homeomorphic to a sphere. This improves a result of S. Gallot and D. Meyer [J. Math. Pures Appl., IX. Sér. 54, 259-284 (1975; Zbl 0316.53036)].
Reviewer: D.Ferus

MSC:
53C20 Global Riemannian geometry, including pinching
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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