Special Hermitian metrics on compact solvmanifolds
By Anna Fino, Luigi Vezzoni. 2015
65 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/eb4770fc4a10180010dbcbf8f74751e0183c7f2b
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In Applied Mathematics
- Fabio Paradiso
- Quanting Zhao
- Anna Fino
- Ramiro A. Lafuente
- Romina M. Arroyo
- Fang Zheng
- Xiaokui Yang
- L. Ugarte
In Geometry and Topology
- Fabio Paradiso
- Quanting Zhao
- Anna Fino
- Ramiro A. Lafuente
- Romina M. Arroyo
- Fang Zheng
- Xiaokui Yang
- L. Ugarte
Citations in the corpus
- The long‐time behavior of the homogeneous pluriclosed flow (2017, result): “Previous results in this regard include a complete description of the long-time behavior of the flow on locally homogeneous compact complex surfaces [4], long-time existence on 2-step nilmanifolds of arbitrary dimension [12], and on two 6-dimensional solvmanifolds [11].”
- Strominger connection and pluriclosed metrics (2019, background): “To state the result, let us first recall the following interesting conjecture of Fino and Vezzoni in non-Kähler geometry: Conjecture 2 (Fino-Vezzoni [12]).”
- Balanced Hermitian structures on almost abelian Lie algebras (2020, background): “This has been confirmed on some special classes of compact complex manifolds: twistor spaces of compact anti-self-dual Riemannian manifolds [56], non-Kähler manifolds belonging to the Fujiki class C [15], a family of non-Kähler Calabi-Yau threefolds constructed in [31], generalized Calabi-Gray manif”