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.
Received: January 2015; Revised: August 2015; Available Online: October 2015.
2015 Impact Factor.6