Ricci curvature and monopole classes on $3$-manifolds

Chanyoung Sung

doi:10.4134/JKMS.2012.49.5.965

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J. Korean Math. Soc. 2012; 49(5): 965-976

Printed September 1, 2012

https://doi.org/10.4134/JKMS.2012.49.5.965

Ricci curvature and monopole classes on $3$-manifolds

Chanyoung Sung

Konkuk University

Abstract

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Abstract

We prove an $L^2$-estimate of Ricci curvature in terms of harmonic 1-forms on a closed oriented Riemannian $3$-manifold admitting a solution of any rescaled Seiberg-Witten equations. We also give a necessary condition to be a monopole class on some special connected sums.

Keywords: Seiberg-Witten equations, Ricci curvature, monopole class

MSC numbers: 57R57, 57M50, 53C99