摘要：

It's shown that on an n-dimensional LCS Lie group, there exist harmonic sections and leftinvariant vector fields defining harmonic maps only when it is endowed with a flat left invariant pseudo-Ri-emannian metric. Moreover, we determine all the vector fields which are critical points of the energy functionalrestricted to vector fields of the same length on the n-dimensional pseudo-Riemannian LCS Lie group.