2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99164I prove that every smooth legendrian variety generated by quadrics is a homogeneous variety and further I give a list of all such legendrian varieties. A review of the subject is included, illustrated by examples. Another result is that no complete intersection is a legendrian variety.44 pages, 11 figures. This is an extended translation of my MSc Degree disertationAlgebraic GeometryRepresentation Theory14M99, 14M10, 14M17 (Primary) 17B10, 22E46 (Secondary)text