Invariant metrics on Lie groups

Gerard Thompson

doi:10.3934/jgm.2015.7.517

Article Contents

2015, Volume 7, Issue 4: 517-526. Doi: 10.3934/jgm.2015.7.517

This issue Previous Article Canonoid and Poissonoid transformations, symmetries and biHamiltonian structures Next Article

Invariant metrics on Lie groups

Gerard Thompson^1,

1.
The University of Toledo, 2801 W Bancroft St., Toledo, OH 43606

Received: December 31, 2014

Revised: July 31, 2015

Published: November 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 22E60, 53B21, 22E27; Secondary: 57S99.

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References

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