Homogeneous and locally homogeneous solutions to symplectic curvature flow

Abstract

J. Streets and G. Tian recently introduced symplectic curvature flow, a geometric flow on almost K\"ahler manifolds generalising K\"ahler-Ricci flow. The present article gives examples of explicit solutions to this flow of non-K\"ahler structures on several nilmanifolds and on twistor fibrations over hyperbolic space studied by J. Fine and D. Panov. The latter lead to examples of non-K\"ahler static solutions of symplectic curvature flow which can be seen as analogues of K\"ahler-Einstein manifolds in K\"ahler-Ricci flow.