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Duality in twistor theory without Minkowski space

Published online by Cambridge University Press:  24 October 2008

M. A. Singer
M. A. Singer
Affiliation:
Mathematical Institute, Oxford 0X1 3LB
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Abstract

A modified form of the generalized Penrose-Ward Transform [4, 6] is set up to investigate the correspondence between twistor space and dual twistor space. The ways in which it differs from the ‘usual’ transform are discussed and it is used to give an alternative proof of Eastwood's recent generalization [7] of the twistor transform [9, 5] which avoids all mention of Minkowski space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 591 - 600
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Bott, R.. Homogeneous vector bundles. Ann. of Math. 66 (1957), 203–248.CrossRefGoogle Scholar
[2]Bott, R. and Tu, L. W.. Differential Forms in Algebraic Topology. Graduate Texts in Maths. Vol. 82 (Springer-Verlag, 1982).CrossRefGoogle Scholar
[3]Buchdahl, N. P.. On the relative de Rham sequence. Proc. Amer. Math. Soc. 87 (1983), 363–366.CrossRefGoogle Scholar
[4]Eastwood, M. G., Penrose, R. and Wells, R. O.. Cohomology and massless fields. Comm. Math. Phys. 78 (1981), 305–351.CrossRefGoogle Scholar
[5]Eastwood, M. G. and Ginsberg, M. L.. Duality in twistor theory. Duke. Math. J. 48 (1981), 177–196.Google Scholar
[6] M.Eastwood, G.. The generalized Penrose-Ward transform. Math. Proc. Cambridge Philos. Soc. 97 (1985), 165–187.CrossRefGoogle Scholar
[7]Eastwood, M. G.. A duality for homogeneous bundles on twistor space. J. London Math. Soc. (to appear).Google Scholar
[8]Godement, R.. Topologie Algébrique et Théorie des Faisceaux. (Hermann, 1958).Google Scholar
[9]Penrose, R. and MacCallum, M. A. H.. Twistor theory: an approach to the quantization of fields and spacetime. Phys. Rep. 6C (1972), 241–316.Google Scholar
[10]Wells, R. O.. Differential Analysis on Complex Manifolds. Graduate Texts in Maths. Vol. 65 (Springer-Verlag, 1980).CrossRefGoogle Scholar