Twistor spinors were introduced by R. Penrose as solutions of a conformally invariant field equations in general relativity. In this paper we consider Riemannian spin manifolds carrying twistor spinors. Outside their zero set they can be seen as conformal analogues of parallel spinors. As an example, a twistor spinor with a zero exists on the standard sphere. Moreover, A. Lichnerowicz proved in [Li, Thm. 7] that the sphere with its standard conformal structure is the only compact Riemannian spin manifold carrying twistor spinors with zeros.
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