2005/10/28 by Felipe Leitner, Leitner, Felipe · 2 citations
Mathematics · #32V05 #53A30 #53B15 #53B30 #53C15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG #msc:32V05 #msc:53A30 #msc:53B15 #msc:53B30 #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0510637
37 pages
openalex publication_date 2005/10/28 · arxiv created 2005/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℓ-Fefferman construction. We show that a certain class of ℓ-Fefferman metrics on partially integrable CR-spaces provides all solutions to our problem concerning the complex structures.