On 4-Dimensional J-Invariant Shrinking Ricci Solitons

2014/01/19 by Frederick Fong, Frederick Tsz-Ho Fong, Fong, Frederick Tsz-Ho
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1401.4748

11 pages

arxiv created 2014/01/19 · arxiv updated 2014/01/21

Abstract

As of today, there are very few known complete shrinking Ricci solitons in dimension 4, and all examples discovered so far are Kähler and/or Einstein. In this note, we prove that any four dimensional J-invariant gradient shrinking Ricci solitons satisfy a differential form identity relating Kählerity annd Einstein-ness.

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