C_{abcd} = ψ_{ABCD} ε_{A′B′} ε_{C′D′} + ψ^{~}_{A′B′C′D′} ε_{AB} ε_{CD}

(i) tangent vectors to α-surfaces are null;

(ii) any two null tangent vectors v and u to an α-surface are orthogonal to one another;

(iv) α-surfaces are self-dual, in that F ≡ v ⊗ u − u ⊗ v takes the two-spinor form;

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