Manifolds with 1/4-Pinched Flag Curvature |
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Authors: | Lei Ni Burkhard Wilking |
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Institution: | 1. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093, USA 2. Mathematisches Institut, University of Münster, Einsteinstrasse 62, 48149, Münster, Germany
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Abstract: | We say that a nonnegatively curved manifold (M, g) has quarter-pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature
is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem
of Brendle and Schoen it follows that any positively curved manifold with strictly quarter-pinched flag curvature must be
a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd-dimensional manifolds we obtain
results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent
work of Petersen and Tao. |
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Keywords: | |
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