Abelian Hermitian geometry

DOI10.1016/j.difgeo.2012.07.001zbMath1253.53025arXiv1106.6268OpenAlexW2089377864WikidataQ115356700 ScholiaQ115356700MaRDI QIDQ714445

Isabel G. Dotti, Adrián Andrada, María Laura Barberis

Publication date: 11 October 2012

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.6268

zbMATH Keywords

Hermitian metricKähler metricabelian complex structuresfirst canonical connection

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Local differential geometry of Hermitian and Kählerian structures (53B35) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (15)

Nearly para-Kähler geometry on Lie groups ⋮ Extending invariant complex structures ⋮ Hyper-para-Kähler Lie algebras with abelian complex structures and their classification up to dimension 8 ⋮ Abelian balanced Hermitian structures on unimodular Lie algebras ⋮ Odd‐dimensional counterparts of abelian complex and hypercomplex structures ⋮ Pluriclosed and Strominger Kähler–like metrics compatible with abelian complex structures ⋮ Locally conformally Kähler solvmanifolds: a survey ⋮ From almost (para)-complex structures to affine structures on Lie groups ⋮ Locally conformally Kähler structures on unimodular Lie groups ⋮ Indefinite hyperkähler metrics on Lie groups with abelian complex structures ⋮ Hermitian curvature flow on unimodular Lie groups and static invariant metrics ⋮ Para-Kähler hom-Lie algebras ⋮ Complex nilmanifolds with constant holomorphic sectional curvature ⋮ Lie groups with flat Gauduchon connections ⋮ SKT and tamed symplectic structures on solvmanifolds

Cites Work

• Abelian para-Kähler structures on Lie algebras
• Chern-flat and Ricci-flat invariant almost Hermitian structures
• Canonical bundles of complex nilmanifolds, with applications to hypercomplex geometry
• Double products and hypersymplectic structures on \(\mathbb R^{4n}\)
• Hermitian structures on six-dimensional nilmanifolds
• Curvatures of left invariant metrics on Lie groups
• On the metric structure of non-Kähler complex surfaces
• Geometry of hyper-Kähler connections with torsion
• Hyper-Kähler quotients of solvable Lie groups
• HyperKähler torsion structures invariant by nilpotent Lie groups
• Complex Connections with Trivial Holonomy
• Classification of abelian complex structures on 6-dimensional Lie algebras
• DEFORMATION OF 2-STEP NILMANIFOLDS WITH ABELIAN COMPLEX STRUCTURES
• Complex product structures on 6-dimensional nilpotent Lie algebras
• STABILITY OF ABELIAN COMPLEX STRUCTURES
• Complex product structures on Lie algebras
• Lie algebras, decomposable into a sum of an Abelian and a nilpotent subalgebra
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