On G-Lie foliations with transverse CR structure

Abstract

We study the interplay between CR structures on real Lie algebras and G-Lie foliations (in the sense of E. Fedida [4]). We show that the transverse KohnRossi cohomology of a complete G-Lie foliation F with transverse CR structure and dense leaves is isomorphic to the Kohn-Rossi cohomology of the structural Lie algebra of F. We classify (up to homotopy) the f-structures in the normal bundle of a G-Lie foliation.

Keywords

• transverse cr structure
• g-lie foliation
• maurer-cartan form
• transverse kohn-rossi cohomology