Rigidity of noncompact complete manifolds with harmonic curvature

2009/11/13 by Seongtag Kim, Kim, Seongtag · 1 citation
Mathematics · Physics and Astronomy · #53C21 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.DG #msc:53C21 #msc:58J05

paper · pdf · doi:10.48550/arxiv.0911.2694

11 page, corrections + updated results

Abstract

Let (M,g) be a noncompact complete n-manifold with harmonic curvature and positive Sobolev constant. Assume that L₂ norms of Weyl curvature and traceless Ricci curvature are finite. We prove that (M,g) is Einstein if n ≥ 5 and L_n/2 norms of Weyl curvature and traceless Ricci curvature are small enough.

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