Transversely Holomorphic Flows on 3-Manifolds and Geodesible Vector Fields
Fawaz, Amine M.
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https://hdl.handle.net/2142/86968
Description
Title
Transversely Holomorphic Flows on 3-Manifolds and Geodesible Vector Fields
Author(s)
Fawaz, Amine M.
Issue Date
1998
Doctoral Committee Chair(s)
Tondeur, Philippe
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
One considers a transversely holomorphic flow on a 3-dimensional manifold. We compute the second fundamental form of the normal distribution and we draw some conclusions, one of which is a global obstruction to the existence of transversely holomorphic flows on 3-manifolds; then an explicit form of the first Chern class of the normal bundle is given when the flow is Riemannian. We study the geodesibility of the projections of basic vector fields onto the normal bundle, in the regular and in the singular case. Finally the topology of the singularities of transversely meromorphic vector fields and meromorphic differential forms is studied.
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