The long-time behaviour of the pluriclosed flow on Lie groups

ROMINA M. ARROYO; RAMIRO A. LAFUENTE

Hanover

Congreso; Lie Group Actions in Riemannian Geometry; 2017

Dartmouth College

The pluriclosed flow is a geometric flow that evolves pluriclosed Hermitian structures (i.e. Hermitian structures for which its 2-fundamental form satisfies $\partial \bar \partial \omega =0$) in a given complex manifold. The aim of this talk is to discuss the asymptotic behaviour of the pluriclosed flow in the case of left-invariant structures on Lie groups. More precisely, invariant structures on nilmanifolds and solvmanifolds. We will analyze the flow and explain how a suitable normalization converges to pluriclosed solitons, which are self-similar solutions to the flow.This is a joint work with Ramiro Lafuente (University of Münster).