Abstract
Electromagnetic curvature structures (c.s.) are defined as being bilinear in the two electromagnetic field matrices and electrovac c.s. by having the el.magn. energy-momentum as Einstein tensor. There is a one-parameter familiy of electrovac c.s. having never a component in the space of constant curvatures. Their non-Weyl component is uniquely determined by the el.magn. energy-momentum, and in general they have a Weyl component. It is shown that el.magn. implies gravitational radiation, and coversely that el.magn. gravitational radiation is induced by el.magn. radiation. A structure theory of c.s. is described with morphisms as linear conformal transformations (i.e. Lorentztransformations and dilatations) such that the above properties of c.s., and many others, are orbit properties.
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Tilgner, H. (1985). Conformal orbits of electromagnetic Riemannian curvature tensors electromagnetic implies gravitational radiation. In: Ferus, D., Gardner, R.B., Helgason, S., Simon, U. (eds) Global Differential Geometry and Global Analysis 1984. Lecture Notes in Mathematics, vol 1156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075101
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DOI: https://doi.org/10.1007/BFb0075101
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