Complete manifolds with nonnegative curvature operator |
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Authors: | Lei Ni Baoqiang Wu |
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Institution: | Department of Mathematics, University of California at San Diego, La Jolla, California 92093 ; Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu, People's Republic of China |
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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 -nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension ) whose curvature operator is bounded and satisfies the pinching condition , for some , must be compact. This provides an intrinsic analogue of a result of Hamilton on convex hypersurfaces. |
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Keywords: | |
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