1. To attach or fasten something very securely to something else, with or as with rivets. A noun or pronoun can be used between "rivet" and "on." We'll need to rivet on a new handle before we'll be able to use this door. They riveted a makeshift ladder on the side of the house.

2. To focus one's attention or gaze on someone or something else. A noun or pronoun is used between "rivet" and "on." I riveted my gaze on the television as the final seconds of the game ticked away. I don't think I could handle celebrity. Having thousands of people rivet their attention on me every day sounds like a nightmare. As I stood atop the Empire State Building, my eyes were riveted on the tiny specks of people on the ground below.