The phrase "riveted the eyes on" implies a strong and unwavering focus on something. Antonyms for this phrase can include words that denote distraction, disinterest, or lack of attention. Some of these antonyms include: averted the gaze, looked away, lost interest, distracted attention, and glanced fleetingly. Other antonyms may include phrases that express uncertainty, hesitation, or a lack of conviction. These can include: wavering attention, unsure focus, uncertain gaze, and tentative observation. Ultimately, the choice of antonym will depend on the context of the sentence and the intended meaning, but all of these words convey a lack of fixation or concentration.