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Einstein-Weyl from Kaluza-Klein. (English) Zbl 1220.83040

Summary: We discuss the Kaluza-Klein reduction of spaces with (anti-)self-dual Weyl tensor and point out the emergence of the Einstein-Weyl equations for the reduction from four to three dimensions. As a byproduct we get a simple expression for the gravitational instanton density in terms of the Kaluza-Klein functions.

MSC:

83E15 Kaluza-Klein and other higher-dimensional theories
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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References:

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