Kählerity of shrinking gradient Ricci solitons asymptotic to Kähler cones

Abstract

We prove that a shrinking gradient Ricci soliton which is asymptotic to a Kähler cone along some end is itself Kähler on some neighborhood of infinity of that end. When the shrinker is complete, it is globally Kähler.

v2: 13 pages, minor changes. To appear in J. Geom. Anal