Symplectic Curvature Flow

JORGE LAURET, CYNTHIA WILL

Wolfach

Workshop; Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions; 2014

Mathematisches Forschungsinstitut Oberwolfach

J. Streets and G. Tian introduced a natural way to evolve an almost-Kahler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all evolving. We study in this paper dierent aspects of the flow on locally homogeneous manifolds, including long-time existence, solitons, regularity and convergence. We develop in detail two classes of Lie groups, which are relatively simple from a structural point of view but yet geometrically rich and exotic: solvable Lie groups with a codimension one abelian normal subgroup and a construction attached to each left symmetric algebra.