Moscow Mathematical Journal

Volume 19, Issue 2, April–June 2019 pp. 275–305.

Palais Leaf-Space Manifolds and Surfaces Carrying Holomorphic Flows

Authors: Ana Cristina Ferreira (1), Julio C. Rebelo (2), and Helena Reis (3)
Author institution:(1) Centro de Matemática da Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
(2) Institut de Mathématiques de Toulouse; UMR 5219, Université de Toulouse, 118 Route de Narbonne, F-31062 Toulouse, FRANCE
(3) Centro de Matemática da Universidade do Porto, Faculdade de Economia da Universidade do Porto, Portugal

Summary:

Given a pair of commuting holomorphic vector fields defined on a neighborhood of (0,0)∈ℂ², we discuss the problem of globalizing them as an action of ℂ² on a suitable complex surfaces along with some related questions. A review of Palais' theory about globalization of local transformation groups is also included in our discussion.

2010 Math. Subj. Class. Primary: 32S65; Secondary: 37F75, 57S20.

Keywords: Holomorphic local transformation groups, foliations and leaf spaces, holomorphic complete vector fields.

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