Classification of solitons for pluriclosed flow on complex surfaces

2018/02/01 by Jeffrey Streets, Streets, Jeffrey · 3 citations
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · doi:10.1007/s00208-019-01887-4

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 Kähler 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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