About complex structures in conformal tractor calculus

The aim of this paper is to describe the geometry of conformal structures in Lorentzian signature, which admit a lightlike conformal Killing vector field whose corresponding adjoint tractor acts as complex structure on the standard tractor bundle of conformal geometry. Key to the treatment of this p...

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Bibliographic Details
Published in:arXiv.org 2005-10
Main Author: Leitner, Felipe
Format: Article
Language:English
Subjects:
Construction
Fields (mathematics)
Geometry
Online Access:Get full text
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Summary:The aim of this paper is to describe the geometry of conformal structures in Lorentzian signature, which admit a lightlike conformal Killing vector field whose corresponding adjoint tractor acts as complex structure on the standard tractor bundle of conformal geometry. Key to the treatment of this problem is CR-geometry and the Fefferman construction. In fact, we will consider here partially integrable CR-structures and a slightly generalised Fefferman construction for these, which we call the \(\ell\)-Fefferman construction. We show that a certain class of \(\ell\)-Fefferman metrics on partially integrable CR-spaces provides all solutions to our problem concerning the complex structures.
ISSN:2331-8422