Special Hermitian metrics on compact solvmanifolds
arXiv:1502.03476 · doi:10.1016/j.geomphys.2014.12.010
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.
arXiv comment16 pages. To appear in a special issue of the Journal of Geometry and Physics
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- A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System
- On Gauduchon connections with Kähler-like curvature
- The long-time behavior of the homogeneous pluriclosed flow
- New supersymmetric vacua on solvmanifolds
- Hermitian Curvature flow on unimodular Lie groups and static invariant metrics
- Hermitian curvature flow on complex homogeneous manifolds
- The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor
- On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics
- On the existence of balanced metrics on six-manifolds of cohomogeneity one
- Blowing up Chern-Ricci flat balanced metrics