The author studies the properties and applications of quasi-Killing spinors and quasi-twistor spinors and obtains some vanishing theorems. In particular, the author classifies all the types of quasi-twistor spinors on closed Riemannian spin manifolds. As a consequence, it is known that on a locally decomposable closed spin manifold with nonzero Ricci curvature, the space of twistor spinors is trivial. Some integrabili...
