Complex product structures on 6-dimensional nilpotent Lie algebras

DOI10.1515/FORUM.2008.015zbMath1176.17006arXivmath/0610768MaRDI QIDQ3516711

Adrián Andrada

Publication date: 11 August 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610768

zbMATH Keywords

nilpotent Lie algebracomplex product structureflat torsion-free connection

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Solvable, nilpotent (super)algebras (17B30)

Related Items

Nearly para-Kähler geometry on Lie groups ⋮ Symplectic, product and complex structures on 3-Lie algebras ⋮ Geometry of paraquaternionic Kähler manifolds with torsion ⋮ COMPLEX PRODUCT STRUCTURES ON HOM-LIE ALGEBRAS ⋮ Four-dimensional Lie algebras with a para-hypercomplex structure ⋮ On deformations of D-manifolds and CR D-manifolds ⋮ Symplectic structures, product structures and complex structures on Leibniz algebras ⋮ Para-Kähler hom-Lie algebras ⋮ Construction of nice nilpotent Lie groups ⋮ Nijenhuis operators, product structures and complex structures on Lie–Yamaguti algebras ⋮ Product and complex structures on hom-Lie superalgebras ⋮ Hyper-para-Hermitian manifolds with torsion ⋮ Abelian Hermitian geometry ⋮ Interpolation of geometric structures compatible with a pseudo Riemannian metric ⋮ Para-Hermitian and paraquaternionic manifolds ⋮ Nijenhuis operators on 3-Hom-L-dendriform algebras

Cites Work

• Double products and hypersymplectic structures on \(\mathbb R^{4n}\)
• Three-dimensional affine crystallographic groups
• Paracomplex structures and affine symmetric spaces
• On the nilpotent Lie algebras of dimension \(\leq 7)\)
• The structure of complete left-symmetric algebras
• Translations in simply transitive affine actions of Heisenberg type Lie groups
• On certain locally homogeneous Clifford manifolds
• Abelian hypercomplex 8-dimensional nilmanifolds
• Complex product structures and affine foliations
• A homogeneous space–time model with singularities
• Simply Transitive Groups of Affine Motions
• Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology
• Complex product structures on Lie algebras
• Complex structures on nilpotent Lie algebras