Hypercomplex structures with Hermitian-Norden metrics on four-dimensional Lie algebras

Abstract

Integrable hypercomplex structures with Hermitian and Norden metrics on Lie groups of dimension 4 are considered. The corresponding five types of invariant hypercomplex structures with hyper-Hermitian metric, studied by M.L. Barberis, are constructed here. The different cases regarding the signature of the basic pseudo-Riemannian metric are considered.

12 pages

References in corpus (3)

• A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics
• Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such structure
• On hypercomplex pseudo-Hermitian manifolds

Cited by in corpus (1)

• Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds