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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 471
Twistor Spinors and Normal Cartan Connections in Conformal Geometries Felipe Leitner
We formulate conformal (spin) geometry with arbitrary signature in the context of almost Hermitian symmetric geometry and construct the canonical normal Cartan connection of conformal geometry. It is shown that twistor spinors on a conformal spin manifold $M$ may be interpreted as parallel sections in a conformal spinor bundle $E o M$ with respect to a covariant derivative $ abla^E$, which arises from the canonical normal Cartan connection. We also describe every conformally flat spin manifold $M$, which admits twistor spinors, with the aid of the holonomy representation of the fundamental group $pi_1(M)$.
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