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Abstract: We say that a nonnegatively curved manifold $M,g$ has quarter pinched flagcurvature if for any two planes which intersect in a line the ratio of theirsectional curvature is bounded above by 4. We show that these manifolds havenonnegative complex sectional curvature. By combining with a theorem of Brendleand Schoen it follows that any positively curved manifold with strictly quarterpinched flag curvature must be a space form. This in turn generalizes a resultof Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtainresults for the case that the flag curvature is pinched with some constantbelow one quarter, one of which generalizes a recent work of Petersen and Tao.



Autor: Lei Ni, Burkhard Wilking

Fuente: https://arxiv.org/







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