The Pluriclosed Flow on Nilmanifolds and Tamed Symplectic Forms
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We study the 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 symplectic forms taming a complex structure, by considering the evolution of symplectic forms via the flow induced by the Bismut Ricci form.
KeywordsHermitian metrics Symplectic forms Nilpotent Lie groups
Mathematics Subject Classification53C15 53B15 53C30
The authors would like to thank Jorge Lauret for useful conversations and the referee for helpful comments on the paper.