The pluriclosed flow on nilmanifolds and Tamed symplectic forms

2012/10/17 by Nicola Enrietti, Enrietti, Nicola, Anna Fino +3 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1210.4816

openalex publication_date 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study evolution of (strong Kähler with torsion) SKT structures via the pluriclosed flow on complex nilmanifolds, i.e. on compact quotients of simply connected nilpotent Lie groups by discrete subgroups endowed with an invariant complex structure. Adapting to our case the techniques introduced by Jorge Lauret for studying Ricci flow on homogeneous spaces we show that for SKT Lie algebras the pluriclosed flow is equivalent to a bracket flow and we prove a long time existence result in the nilpotent case. Finally, we introduce a natural flow for evolving tamed symplectic forms on a complex manifold, by considering evolution of symplectic forms via the flow induced by the Bismut Ricci form.

Cited by

• Complex structures on 2-step nilpotent Lie algebras arising from graphs
• Positive Hermitian curvature flow on 2-step nilpotent Lie groups

Related

• Pluriclosed flow and Hermitian-symplectic structures
• The Ricci Flow for Nilmanifolds
• Generalized Ricci flow on nilpotent Lie groups
• The Ricci flow for simply connected nilmanifolds
• The Ricci-Bourguignon flow on Heisenberg and quaternion Lie groups