Abstract
The three-surface twistor equation is defined for an arbitrary three-surface Σ in an arbitrary curved spaceM. It is proved that three-surface twistors exist on 2 if and only if Σ can be embedded in a conformally flat space-time with the same first and second fundamental forms.
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Tod, K.P. Three-surface twistors and conformal embedding. Gen Relat Gravit 16, 435–443 (1984). https://doi.org/10.1007/BF00762335
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DOI: https://doi.org/10.1007/BF00762335