Local differential geometry of null curves in conformally flat space-time

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Abstract
The conformally invariant differential geometry of null curves in conformally flat space‐times is given, using the six‐vector formalism, which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: first, sometimes the description is easier in twistor terms and sometimes in six‐vector terms, which leads to a mutual enlightenment of both; and, second, the case of null curves in timelike pseudospheres or 2+1 Minkowski space could only be treated twistorially, making use of an invariant differential found by Fubini and Čech [Geometria Proiettiva Differenziale (Zanichelli, Bologna, 1926), Vol. 1; Introduction à la Géométrie Projective Differentielle des Surfaces (Gauthier–Villars, Paris, 1931)]. The result is the expected one: apart from the stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures that, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations.

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