Abstract
There is an SO(3, 3)-invariant integral transform mapping volume forms on ℝP 3 into two-forms on the conformal compactification of ℝ2.2. The range of this transform is the space self-dual solutions of the ℝ2.2 Maxwell's equations. Moreover, using this transform, one gets a simple description of the null solutions of Maxwell's equations, analogous to the Robinson-Kerr description of the null solutions of Maxwell's equations on ℝ3, 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bott, R. and Tu, L., Differential Forms in Algebraic Topology, Springer-Verlag, New York, 1982.
DeRham, G., Variétés différentiables, Hermann, Paris, 1960.
Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978.
Guillemin, V., ‘On Some Results of Gelfand in Integral Geometry’, Proceedings of Symposia in Pure Math. 43, 149–155 (1985).
John, F., ‘The Ultrahyperbolic Differential Equation with Independent Variables’, Duke Math. J. 4, 300–322 (1938).
Penrose, R., ‘Twistor Algebra’, J. Math. Phys. 8, 345–366 (1967).
Wells, R. O.Jr., ‘Complex Manifolds and Mathematical Physics’, Bull. A.M.S. 1, 296–336 (1979).
Kostant, B., ‘The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group’, Amer. J. Math. 81, 973–1032 (1959).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guillemin, V., Sternberg, S. An ultra-hyperbolic analogue of the Robinson-Kerr theorem. Lett Math Phys 12, 1–6 (1986). https://doi.org/10.1007/BF00400297
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00400297