Four-dimensional Lie algebras with a para-hypercomplex structure

DOI10.1216/RMJ-2010-40-5-1391zbMath1207.53071OpenAlexW2028623667MaRDI QIDQ613522

Srdjan Vukmirović, Novica Blažić

Publication date: 21 December 2010

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2010-40-5-1391

zbMATH Keywords

almost complex structureintegrable structureanti-self-dual metricfour-dimensional Lie algebraalmost product structureholonomy algebras classificationinvariant geometric structures on Lie groupspara-hypercomplex structuresignature (2,2)-metric

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Other complex differential geometry (53C56) Homogeneous complex manifolds (32M10)

Related Items

Extending invariant complex structures ⋮ Geometry of paraquaternionic Kähler manifolds with torsion ⋮ On the geometry of para-hypercomplex 4-dimensional Lie groups ⋮ From almost (para)-complex structures to affine structures on Lie groups ⋮ Unnamed Item ⋮ A complete classification of four-dimensional para-Kähler Lie algebras ⋮ Generalized geometric structures on complex and symplectic manifolds ⋮ COMPLEX AND PARACOMPLEX STRUCTURES ON HOMOGENEOUS PSEUDO-RIEMANNIAN FOUR-MANIFOLDS ⋮ Hyper-para-Hermitian manifolds with torsion ⋮ LEFT INVARIANT $(\alpha,\beta)$-METRICS ON 4-DIMENSIONAL LIE GROUPS

Cites Work

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• Invariant complex structures on four-dimensional solvable real Lie groups
• Geometric structures on compact complex analytic surfaces
• Invariant complex structures on solvable real Lie groups
• Hypersymplectic Lie algebras
• Para-Hermitian and paraquaternionic manifolds
• Product structures on four dimensional solvable Lie algebras
• Hypercomplex structures on four-dimensional Lie groups
• Complex product structures on 6-dimensional nilpotent Lie algebras