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Title: Four-manifolds of pinched sectional curvature
In this paper, we study closed four-dimensional manifolds. In particular, we show that under various pinching curvature conditions (for example, the sectional curvature is no more than 5 6 of the smallest Ricci eigenvalue), 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.  more » « less
Award ID(s):
2104988
PAR ID:
10329200
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Pacific journal of mathematics
ISSN:
0030-8730
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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