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Twistor spaces for real four-dimensional Lorentzian manifolds
Nagoya mathematical journal
It is R. Penrose who constructed the twistor theory which gives a correspondence between complex space-times and 3-dimensional complex manifolds called twistor spaces. He and his colleagues investigated conformally invariant equations (e.g. massless field equations, self-dual Yang-Mills equations) on the space-time by transforming them into objects in complex analytical geometry. See e.g. Penrose-Ward [P-W] or Ward-Wells [W-W]. After that, Atiyah-Hitchin-Singer ([A-H-S], cf. [Fr]) constructeddoi:10.1017/s0027763000004888 fatcat:odk3nsnvqnefbix5xqpllh73ui