The equivalence problem for complex foliations of complex surfaces (Q1116126)

The Cartan equivalence problem for non-holomorphic foliations of complex surfaces is solved in this paper by constructing a natural trivialization of the tangent bundle of the bundle of frames adapted to the foliation. This trivialization can be interpreted as an sl(3,\({\mathbb{R}})\)-valued Cartan connection. It is shown that the foliation of the complement of \({\mathbb{R}}{\mathbb{P}}^ 2\) in \({\mathbb{C}}{\mathbb{P}}^ 2\) by the set of complex lines which intersect \({\mathbb{R}}{\mathbb{P}}^ 2\) in a real line is flat and has SL(3,\({\mathbb{R}})\) as its group of automorphisms.