2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216207We discuss a canonical formalism method for constructing actions describing propagation of W-strings on curved backgrounds. The method is based on the construction of a representation of the W-algebra in terms of currents made from the string coordinates and the canonically conjugate momenta. We construct such a representation for a W_3-string propagating in the background metric with one flat direction by using a simple ansatz for the W-generators where each generator is a polynomial of the canonical currents and the veilbeins. In the case of a general background we show that the simple polynomial ansatz fails, and terms containing the veilbein derivatives must be added.10 pages, Latex, no figures. Revised version (the incorrect result following from a wrong interpretation of a vielbein constraint has been corrected)High Energy Physics - Theorytext