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arXiv · 1502.03476

Special Hermitian metrics on compact solvmanifolds

Anna Fino·Luigi Vezzoni
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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.

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Anna Fino, Luigi Vezzoni. 2015-02-11. Special Hermitian metrics on compact solvmanifolds. https://doi.org/10.1016/j.geomphys.2014.12.010

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