Symplectic curvature flow revisited

TL;DR

This paper revisits the symplectic curvature flow, providing new evolution formulas for key quantities and extending the characterization of its fixed points, thereby deepening understanding of this geometric flow on symplectic manifolds.

Contribution

It introduces new formulas for the evolution of canonical quantities and extends the characterization of fixed points in the symplectic curvature flow.

Findings

New evolution formulas for Chern-related quantities

Extended characterization of fixed points of the flow

Deeper understanding of symplectic curvature flow dynamics

Abstract

We continue studying a parabolic flow of almost K\"{a}hler structures introduced by Streets and Tian which naturally extends K\"{a}hler-Ricci flow onto symplectic manifolds. In the system of primarily the symplectic form, almost complex structure, Chern torsion and Chern connection, we establish new formulas for the evolutions of canonical quantities, in particular those related to the Chern connection. Using this, we give an extended characterization of fixed points of the flow originally performed by Streets and Tian.