The classification of left-invariant para-Kähler structures on simply connected four-dimensional Lie groups

Abstract

We give a complete classification of left invariant para-Kähler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some curvatures properties of the canonical connection associated to these structures as flat, Ricci flat and existence of Ricci solitons.

Keywords

• symplectic lie algebras
• para-kähler structures
• ricci soliton
• 53d05
• 53c30
• 53c25