Classification of solitons for pluriclosed flow on complex surfaces

Jeffrey Streets

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arXiv · 1802.00170

Classification of solitons for pluriclosed flow on complex surfaces

Jeffrey Streets

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Abstract

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be K\"ahler except for the possibility of steady solitons on minimal Hopf surfaces. Then, we construct steady solitons on all class $1$ Hopf surfaces by exploiting a natural symmetry ansatz.

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Jeffrey Streets. 2018-02-01. Classification of solitons for pluriclosed flow on complex surfaces. https://arxiv.org/abs/1802.00170

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