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The concept of Killing spinor is analyzed in a general way by using the spinorial formalism. It is shown, among other things, that higher derivatives of Killing spinors can be expressed in terms of lower order derivatives. Conformal Killing vectors are studied in some detail in the light of spinorial analysis: Classical results are formulated in terms of spinors. A theorem on Lie derivatives of Debever–Penrose vectors is proved, and it is shown that conformal motion in vacuum with zero cosmological constant must be homothetic, unless the conformal tensor vanishes or is of type N. Our results are valid for either real or complex space–time manifolds.
Hacyan et al. (Wed,) studied this question.
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