Abstract
In this paper, we consider a fourth-order gradient flow of the quadratic Riemannian functional ɛ of traceless Ricci curvature on closed 3 -manifolds with a fixed conformal class. We show that the L 2-curvature pinching locally conformally flat 3-manifolds can be deformed to space forms through such gradient flow. More precisely, for the suitable small initial energy functional ɛ, the gradient flow exists for all times and converges smoothly to space forms as the time goes to infinity. As a consequence, we prove the stability for any background metric whose such gradient flow converges to an Einstein metric.
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Mathematics Subject Classifications (2000): Primary: 53C21; Secondary: 58JOS.
Communicated by: Claude LeBrun (Stony Brook)
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Chang, SC. Three-manifolds with small L 2-norm of traceless-Ricci curvature pinching. Ann Glob Anal Geom 30, 37–63 (2006). https://doi.org/10.1007/s10455-006-9021-0
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DOI: https://doi.org/10.1007/s10455-006-9021-0