Foliations with Transversal Quaternionic Structures

Simple item page
dc.creatorPiccinni, Paolo
dc.creatorVaisman, Izu
dc.date2000-01-11
dc.date.accessioned2026-07-07T04:33:17Z
dc.date.available2026-07-07T04:33:17Z
dc.descriptionWe consider manifolds equipped with a foliation $\cal F$ of codimension $4q$, and an almost quaternionic structure $Q$ on the transversal bundle of ${\cal F}$. After discussing conditions of projectability and integrability of $Q$, we study the transversal twistor space $Z{\cal F}$ which, by definition, consists of the $Q$-compatible almost complex structures. We show that $Z{\cal F}$ can be endowed with a lifted foliation ${\hat {\cal F}}$ and two natural almost complex structures $J_1$, $J_2$ on the transversal bundle of $\hat{\cal F}$. We establish the conditions which ensure the projectability of $J_1$ and $J_2$, and the integrability of $J_{1}$ ($J_{2}$ is never integrable).
dc.descriptionLaTex, 36 pages
dc.identifierhttps://arxiv.org/abs/math/0001059
dc.identifierhttp://arxiv.org/abs/math/0001059
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58517
dc.subjectDifferential Geometry
dc.subject53C12; 57R30
dc.titleFoliations with Transversal Quaternionic Structures
dc.typetext

Files

Collections

arXiv