Canonical connections on Riemannian symmetric spaces and solutions to the Einstein-Yang-Mills equations

J. Harnad, J. Tafel B, S. Shnider

Research output: Contribution to journalArticlepeer-review

Abstract

It is shown that for any principal bundle over a Riemannian symmetric space G /G0 which admits G as automorphism group, the canonical G-invariant connection satisfies the source free gauge field equations. Extending this to product manifolds V × G /G0 and assuming the metric and gauge fields decompose in a natural way, this result is still valid and the Einstein equations with gauge fields as source may also be satisfied. For G /G0, this is so automatically, but with a cosmological term present. For dimV = 1 or 2, solutions are found, yielding metrics of the Robertson-Walker and Reissner-Nordstrom type.

Original languageEnglish
Pages (from-to)2236-2240
Number of pages5
JournalJournal of Mathematical Physics
Volume21
Issue number8
DOIs
StatePublished - 1979
Externally publishedYes

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