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arXiv · 1809.05158

Four-manifolds of Pinched Sectional Curvature

Xiaodong Cao·Hung Tran
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Abstract

In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then the manifold is definite. If restricting to a metric with harmonic Weyl tensor, then it must be self-dual or anti-self-dual under the same conditions. Similarly, if restricting to an Einstein metric, then it must be either the complex projective space with its Fubini-Study metric, the round sphere or their quotients. Furthermore, we also classify Einstein manifolds with positive intersection form and an upper bound on the sectional curvature.

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Xiaodong Cao, Hung Tran. 2019-08-08. Four-manifolds of Pinched Sectional Curvature. https://doi.org/10.2140/pjm.2022.319.17

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