K\"ahlerity of complete almost-K\"ahler gradient shrinking Ricci solitons

Junming Xie

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arXiv · 2609.00840

K\"ahlerity of complete almost-K\"ahler gradient shrinking Ricci solitons

Junming Xie

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Abstract

In this paper, we prove that any complete, compact or noncompact, almost-K\"ahler gradient shrinking Ricci soliton is K\"ahler in arbitrary even dimension. Among other applications, combining our result with the classification of complete K\"ahler-Ricci shrinker surfaces, we obtain a full classification of complete almost-K\"ahler gradient shrinking Ricci solitons in real dimension four.

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Junming Xie. 2026-09-01. K\"ahlerity of complete almost-K\"ahler gradient shrinking Ricci solitons. https://arxiv.org/abs/2609.00840

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