On the twistor-spinors

Two interesting conformal invariants which are constant on the manifold are given for twistor-spinors on a spin manifold following the notion of a twistor-spinor associated to a twisted spin bundle. For a twisted spin bundle corresponding to a flat Hermitian vector bundle, the associated twistor-spinors admit the same conformal invariants. An analysis is made of the twistor-spinors ψ given bY Δψ+(f/n)γψ=0, where f is a complex-valued function. There is only one case where ψ is not a Killing spinor. An example is given of a compact spin manifold for which the situation is realized. (orig.)