  Benefiting from the index spinorial formalism, the Killing spinor equation is
integrated in six-dimensional spacetimes. The integrability conditions for the
existence of a Killing spinor are worked out and the Killing spinors are
classified in two algebraic types, in the first type the scalar curvature of
the spacetime must be negative, while in the second type the spacetime must be
an Einstein manifold. In addition, the equations that define Killing-Yano (KY)
and closed conformal Killing-Yano (CCKY) tensors are expressed in the index
notation and, as consequence, all non-vanishing KY and CCKY tensors that can be
generated from a Killing spinor are made explicit.
