Establishes long-time existence of the pluriclosed flow on nilmanifolds, almost-abelian solvmanifolds, and holomorphic torus bundles via a general theorem on holomorphic submersions.
Barbaro , Bismut Hermitian Einstein metrics and the stability of the p luriclosed flow
4 Pith papers cite this work. Polarity classification is still indexing.
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Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
Every homogeneous hypercomplex manifold with transitive compact Lie group action admits a unique invariant HKT-Einstein metric up to scaling, and invariant strong HKT metrics have Bismut-parallel torsion and curvature.
Complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, together with a splitting theorem for compact pluriclosed Calabi-Yau-with-torsion manifolds.
citing papers explorer
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Long-time existence of the pluriclosed flow on some fibrations
Establishes long-time existence of the pluriclosed flow on nilmanifolds, almost-abelian solvmanifolds, and holomorphic torus bundles via a general theorem on holomorphic submersions.
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A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
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On homogeneous HKT manifolds and the Einstein condition
Every homogeneous hypercomplex manifold with transitive compact Lie group action admits a unique invariant HKT-Einstein metric up to scaling, and invariant strong HKT metrics have Bismut-parallel torsion and curvature.
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Pluriclosed manifolds with parallel Bismut torsion
Complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, together with a splitting theorem for compact pluriclosed Calabi-Yau-with-torsion manifolds.