Cocalibrated structures on Lie algebras with a codimension one Abelian ideal

DOI10.1007/s10455-012-9326-0zbMath1259.53047arXiv1109.4774OpenAlexW1974280359MaRDI QIDQ694722

Marco Freibert

Publication date: 13 December 2012

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4774

zbMATH Keywords

exotic holonomycocalibrated structuresLie algebras with codimension-one Abelian idealsspecial geometry on Lie algebras

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05) Issues of holonomy in differential geometry (53C29) Calibrations and calibrated geometries (53C38)

Related Items (18)

Solvable groups and a shear construction ⋮ \({\mathrm {SU}}(4)\)-holonomy via the left-invariant hypo and Hitchin flow ⋮ Cocalibrated \(\mathrm G_2\)-structures on products of four- and three-dimensional Lie groups ⋮ The structure of almost Abelian Lie algebras ⋮ Half-flat structures on indecomposable Lie groups ⋮ Hypercomplex almost abelian solvmanifolds ⋮ Purely coclosed G₂‐structures on nilmanifolds ⋮ Compact solvmanifolds with calibrated and cocalibrated \(\mathrm{G}_2\)-structures ⋮ Harmonic \(\operatorname{G}_2\)-structures on almost abelian Lie groups ⋮ Almost abelian Lie groups, subgroups and quotients ⋮ Holonomy groups of ${{G}_{2}^*}$-manifolds ⋮ On the relation between \(G_2^*\) structures and almost paracontact structures ⋮ The shear construction ⋮ The Laplacian coflow on almost-abelian Lie groups ⋮ Diagram involutions and homogeneous Ricci-flat metrics ⋮ Closed \({\mathrm{G}}_2\)-structures on non-solvable Lie groups ⋮ Weyl-Einstein structures on conformal solvmanifolds ⋮ \(G_2\)-structures on flat solvmanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations
• Spaces admitting homogeneous \(G_{2}\)-structures
• Metrics with exceptional holonomy
• The geometry of three-forms in six dimensions.
• Half-flat structures on products of three-dimensional Lie groups
• Classification des formes trilineaires alternees en dimension 6
• Half-flat structures and special holonomy
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations
• Real trivectors of rank seven
• Universality of Rank 6 Plücker relations and Grassmann cone preserving maps

This page was built for publication: Cocalibrated structures on Lie algebras with a codimension one Abelian ideal