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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BTP manifolds are characterized by an algebraic condition on the Bismut curvature tensor alone, with examples and a classification theorem for non-balanced threefolds.
Complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, together with a splitting theorem for compact pluriclosed Calabi-Yau-with-torsion manifolds.
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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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Curvature characterization of Hermitian manifolds with Bismut parallel torsion
BTP manifolds are characterized by an algebraic condition on the Bismut curvature tensor alone, with examples and a classification theorem for non-balanced threefolds.
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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.