In this paper we construct new Riemannian metrics with positive isotropic curvature on compact manifolds which fiber over the circle. We also study the relationship between the positivity of the isotropic curvature and the positivity of the p-curvature.
In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional Kähler manifold M of positive and bounded holomorphic bisectional curvature, suppose its geodesic balls have Euclidean volume growth and its scalar curvature decays to zero at infinity in the average sense, then M is biholomorphic to C 2 . During the proof, we also discover an interesting gap phenomenon which says that a Kähler manifold as above automatically has quadratic curvature decay at infinity in the average sense.
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