On 4-Dimensional J-Invariant Shrinking Ricci Solitons
Abstract
As of today, there are very few known complete shrinking Ricci solitons in dimension 4, and all examples discovered so far are K\"ahler and/or Einstein. In this note, we prove that any four dimensional J-invariant gradient shrinking Ricci solitons satisfy a differential form identity relating K\"ahlerity annd Einstein-ness.
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