Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898473 | Journal of Geometry and Physics | 2015 | 14 Pages |
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 JJ 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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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Anna Fino, Luigi Vezzoni,