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Invariant metrics on Lie groups

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  • Index formulas for the curvature tensors of an invariant metric on a Lie group are obtained. The results are applied to the problem of characterizing invariant metrics of zero and non-zero constant curvature. Killing vector fields for such metrics are constructed and play an important role in the case of flat metrics.
    Mathematics Subject Classification: Primary: 22E60, 53B21, 22E27; Secondary: 57S99.

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