Una relativa reducida es una relativa especificativa a la que le quitas el pronombre y el auxiliar para que suene más ágil y natural. Si la acción es activa, el verbo pasa a -ing (the man who is waiting → the man waiting); si es pasiva, pasa a participio (the book which was written → the book written). Es un recurso muy típico del inglés escrito y de quien da un salto de nivel: dice lo mismo con menos palabras.
Cómo se reduce
ENThe book that is on the table → the book on the table
ESThe book that is on the table → the book on the table
ENA man who was wearing a hat → a man wearing a hat
ESA man who was wearing a hat → a man wearing a hat
ENA novel which was written by Cervantes → a novel written by Cervantes
ESA novel which was written by Cervantes → a novel written by Cervantes
ENAlso without "be": a friend who lives here → a friend living here; negative: people who don't exercise → people not exercising.
ESTambién sin "be": a friend who lives here → a friend living here; en negativo: people who don't exercise → people not exercising.
El error típico del hispanohablante
Activa → -ing, pasiva → participio: the people living here vs the letter sent yesterday. No los mezcles.
Solo se puede reducir cuando el pronombre es el sujeto de su oración.