Complete manifolds with nonnegative curvature operator

2006/07/14 by Lei Ni, Ni, Lei, WU Bao-qiang +1 · 5 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/0607356

Abstract

In this short note, as a simple application of the strong result proved recently by Böhm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension ≥ 3) whose curvature operator is bounded and satisfies the pinching condition R≥ δR_I>0, for some δ>0, must be compact. This provides an intrinsic analogue of a result of Hamilton on convex hypersurfaces.

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• Decomposition of the Curvature Operator and Applications to the Hopf Conjecture
• Garding cones and positivity of curvature operators

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