"Keep under one's eye" is a synonym for monitoring or keeping a close watch on something or someone. Other synonyms include keeping tabs on, observing, scrutinizing, surveying, supervising, and overseeing. These words imply an active awareness and attention to the actions or movements of the subject, ensuring that they are staying on track or meeting certain expectations. It can also connote a sense of protection, as if the subject being watched is being safeguarded from potential harm or danger. Overall, these synonyms highlight the importance of being vigilant and attentive, both in terms of managing tasks or projects and ensuring the safety and well-being of others.
