Killing's equations for invariant metrics on Lie groups
Firas Hindeleh Gerard Thompson
This article is the first in a series that will investigate symmetry and curvature properties of a right-invariant metric on a Lie group. This paper will consider Lie groups in dimension two and three and will focus on the solutions of Killing's equations. A striking result is that several of the three-dimensional Lie groups turn out to be spaces of constant curvature.
keywords: right-invariant Riemannian metric Lie algebra Killing vector field. Lie group
Invariant metrics on Lie groups
Gerard Thompson
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: invariant Riemannian metric Killing vector field. Lie algebra Lie group

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