Hypercomplex structures on four-dimensional Lie groups. (English) Zbl 0882.53047

Barberis, María Laura

Proc. Am. Math. Soc. 125, No. 4, 1043-1054 (1997).

The author lists all 4-dimensional real Lie groups admitting a left-invariant hypercomplex structure (these are the additive and the multiplicative groups of quaternions and some solvable groups) and classifies all such structures up to conjugacy under automorphisms of groups. The corresponding left-invariant hyperhermitian metrics are also determined.

Reviewer: A.L.Onishchik (Yaroslavl)

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
32M10	Homogeneous complex manifolds
53C56	Other complex differential geometry

Keywords:

hypercomplex structure; hyperhermitian metric