Harmonicity properties of invariant vector fields on three-dimensional Lorentzian Lie groups
Let \(G\) be a three-dimensional, simply connected Lie group with a left-invariant Lorentzian metric; \(TG\) is endowed with the Sasaki metric. This paper investigates whether left-invariant vector fields, as maps from \(G\) to \(TG\), define harmonic mappings. Considering in turn each of the possible Lie algebras in this framework, the author studies left-invariant critical points of the ``energy'' \(E\), and of \(E\) restricted to vector fields, or to vector fields of the same constant length for instance.
scientific article; zbMATH DE number 5862871
scientific article