About Complex Structures in Conformal Tractor Calculus
نویسنده
چکیده
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 CRspaces provides all solutions to our problem concerning the complex structures.
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