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The geometry of P, the bundle of null directions over an Einstein space-time,is studied. The full set of invariants of the natural G-structure on P isconstructed using the Cartan method of equivalence. This leads to an extensionof P which is an elliptic fibration over the space-time. Examples are givenwhich show that such an extension, although natural, is not unique. Areinterpretation of the Petrov classification in terms of the fibres of anextension of P is presented.Comment: LaTex file, accepted in CQ

Extensions of bundles of null directions