Static solutions to symplectic curvature flow in dimension four

TL;DR

This paper characterizes static solutions to symplectic curvature flow in four dimensions, proving they are Kahler-Einstein and establishing local existence of solitons using differential systems analysis.

Contribution

It provides a normal form for static solutions and proves local existence and generality of symplectic curvature flow solitons in four dimensions.

Findings

Complete static solutions are Kahler-Einstein.

Normal form derived in terms of holomorphic data.

Local existence of solitons established via Cartan-Kahler theorem.

Abstract

This article studies special solutions to symplectic curvature flow in dimension four. Firstly, we derive a local normal form for static solutions in terms of holomorphic data and use this normal form to show that every complete static solution to symplectic curvature flow in dimension four is Kahler-Einstein. Secondly, we perform an exterior differential systems analysis of the soliton equation for symplectic curvature flow and use the Cartan-Kahler theorem to prove a local existence and generality theorem for solitons.