Ricci curvature and monopole classes on 3-manifolds

2009/03/03 by Chanyoung Sung, Sung, Chanyoung
Mathematics · #53C99 #57M50 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C99 #msc:57M50 #msc:57R57

paper · pdf · doi:10.48550/arxiv.0903.0417

arxiv created 2012/05/17 · arxiv updated 2012/05/18

Abstract

We prove an L²-estimate involving Ricci curvature and a harmonic 1-form 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.

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