Abstract
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 \(\Delta \psi + \left( {{f \mathord{\left/ {\vphantom {f n}} \right. \kern-\nulldelimiterspace} n}} \right)\gamma \psi = 0\), 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.
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