2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111404The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to rotation groups with arbitrary quadrics as orbits.22 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. For other papers on the same topic, view the publication pages at http://theo.inrne.bas.bg/~bozho/Differential GeometryMathematical Physics53B99, 38A17, 58J70 34A26, 34A99text