The Journal of Geometric Mechanics (JGM)

Invariant metrics on Lie groups

Pages: 517 - 526, Volume 7, Issue 4, December 2015      doi:10.3934/jgm.2015.7.517

       Abstract        References        Full Text (369.5K)       Related Articles       

Gerard Thompson - The University of Toledo, 2801 W Bancroft St., Toledo, OH 43606, United States (email)

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.

Keywords:  Lie algebra, Lie group, invariant Riemannian metric, Killing vector field.
Mathematics Subject Classification:  Primary: 22E60, 53B21, 22E27; Secondary: 57S99.

Received: January 2015;      Revised: August 2015;      Available Online: October 2015.