Foliations with transversal quaternionic structures

Paolo Piccinni, Izu Vaisman

Research output: Contribution to journalArticlepeer-review


We consider manifolds equipped with a foliation T of codimension 4q, and an almost quaternionic structure g on the transversal bundle of P'. After discussing conditions of projectability and integrability of Q, we study the transversal twistor space Zf which, by definition, consists of the Q-compatible almost complex structures. We show that Zf can be endowed with a liftedjbliation F and two natural almost complex structures J\, Ji on the transversal bundle of y'. We establish the conditions which ensure the projectability of J1 and J2, and the integrability of J1 (J2 is never integrable).

Original languageEnglish
Pages (from-to)303-330
Number of pages28
JournalAnnali di Matematica Pura ed Applicata
Issue number3
StatePublished - 2001
Externally publishedYes


  • Foliation
  • Quaternionic structure
  • Twistor space

ASJC Scopus subject areas

  • Applied Mathematics


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