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Twistor spaces for real four-dimensional Lorentzian manifolds

Published online by Cambridge University Press:  22 January 2016

Yoshinori Machida  and
Hajime Sato
Yoshinori Machida
Affiliation:
Numazu College of Technology, 3600 Ooka Numazu-shi, Shizuoka 410, Japan
Hajime Sato
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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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]) constructed the twistor spaces corresponding to real 4-dimensional Riemannian manifolds. Their construction as well as that of Penrose is mainly effective under the condition of the self-duality. In this paper we will construct twistor spaces more geometrically from real 4-dimensional Lorentzian manifolds under a suitable curvature condition.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 134 , June 1994 , pp. 107 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

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