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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 883–909 | Cite as

The Pluriclosed Flow on Nilmanifolds and Tamed Symplectic Forms

  • Nicola Enrietti
  • Anna Fino
  • Luigi VezzoniEmail author
Article

Abstract

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.

Keywords

Hermitian metrics Symplectic forms Nilpotent Lie groups 

Mathematics Subject Classification

53C15 53B15 53C30 

Notes

Acknowledgements

The authors would like to thank Jorge Lauret for useful conversations and the referee for helpful comments on the paper.

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Dipartimento di Matematica G. PeanoUniversità di TorinoTorinoItaly

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