## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

JGM

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.

JGM

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.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]