Certain symmetries of ${\mathbb{R}}^2$ with diagonal metrics

Abstract

We put into light the Killing vector fields on ${\mathbb{R}}^2$ endowed with a family of diagonal Riemannian metrics. According to certain restrictions on the Lamé coefficients, we concretely describe the symmetries of the metric.

12 pages

References in corpus (1)

• Killing vector fields and a homogeneous isotropic universe

Cited by in corpus (1)

• Constructing Ricci vector fields on ${\mathbb{R}}^2$ with a diagonal metric