Samuel Lockman: Classification of semi-Riemannian Spin^c Manifolds carrying Generalised Killing Spinors

I aim to present the following main result of my thesis: every Lorentzian spin^c manifold carrying a real Killing spinor, that satisfies some rather mild completeness assumption, is isometric to a warped product. With previous results by Bohle, we now have a complete description of all Lorentzian spin manifolds with real Killing spinors, improving the latest results by Leistner.

Further, without any completeness assumptions, we apply results by Kühnel and Rademacher, to describe the local geometry of semi-Riemannian spin^c manifolds with generalised Killing spinors, in many cases. In this spirit, inspired by the work of Gutiérrez and Olea, we give conditions on specific neighbourhoods of the manifold which are isometric to a warped product. Also, we give conditions for when a semi-Riemannian spin^c manifold carrying a generalised Killing spinor has a normal semi-Riemannian covering in the form of a warped product. With this, one for example obtains improvements of the classification by Große and Nakad of Riemannian spin^c manifolds with imaginary generalised Killing spinors.