Abstract
We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature (2,n−2). Derived geometries include Brinkmann spaces, Lorentzian Einstein–Sasaki spaces and certain warped product structures. Exceptional cases with decomposable holonomy of the cone are possible.
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