Oka principle for Levi flat manifolds

  • Samuele MongodiEmail author
  • Giuseppe Tomassini


The name of Oka principle, or Oka–Grauert principle, is traditionally used to refer to the holomorphic incarnation of the homotopy principle: on a Stein space, every problem that can be solved in the continuous category, can be solved in the holomorphic category as well. In this note, we begin the study of the same kind of questions on a Levi-flat manifold; more precisely, we try to obtain a classification of CR-bundles on a semiholomorphic foliation of type (n, 1). Our investigation should only be considered a preliminary exploration, as it deals only with some particular cases, either in terms of regularity or bidegree of the bundle, and partial results.

Mathematics Subject Classification

14D22 14D23 18G55 18G30 32Q45 


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Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Scuola Normale SuperiorePisaItaly

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