We review some constructions and properties of complex manifolds admitting pluriclosed and balanced metrics. We prove that for a 6-dimensional solvmanifold endowed with an invariant complex structure J having holomorphically trivial canonical bundle the pluriclosed flow has a long time solution for every invariant initial datum. Moreover, we state a new conjecture about the existence of balanced and SKT metrics on compact complex manifolds. We show that the conjecture is true for nilmanifolds of dimension 6 and 8 and for 6-dimensional solvmanifolds with holomorphically trivial canonical bundle.

Special Hermitian metrics on compact solvmanifolds

FINO, Anna Maria;VEZZONI, Luigi
2015-01-01

Abstract

We review some constructions and properties of complex manifolds admitting pluriclosed and balanced metrics. We prove that for a 6-dimensional solvmanifold endowed with an invariant complex structure J having holomorphically trivial canonical bundle the pluriclosed flow has a long time solution for every invariant initial datum. Moreover, we state a new conjecture about the existence of balanced and SKT metrics on compact complex manifolds. We show that the conjecture is true for nilmanifolds of dimension 6 and 8 and for 6-dimensional solvmanifolds with holomorphically trivial canonical bundle.
2015
91
-
40
53
http://www.sciencedirect.com/science/article/pii/S0393044014002721
http://arxiv.org/pdf/1502.03476.pdf
Hermitian metrics, Symplectic forms, Nilpotent Lie groups
A. Fino; L. Vezzoni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/150817
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