The equivalence problem for complex foliations of complex surfaces
type: Item
instance of: scholarly article
title: The equivalence problem for complex foliations of complex surfaces
zbMATH Open document ID: 0665.57023
author: Morris Kalka
author: Thomas E. Duchamp
published in: Illinois Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 32L99
zbMATH DE Number: 4088534
zbMATH Keywords: Monge-Ampère foliations
zbMATH Keywords: Cartan equivalence problem
zbMATH Keywords: non-holomorphic foliations of complex surfaces
zbMATH Keywords: bundle of frames adapted to the foliation
zbMATH Keywords: sl(3,\({\mathbb{R}})\)-valued Cartan connection
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4088534