The phrase "fixed on" means to be focused or attentive towards something or someone. There are several other synonyms that one can use to express the same meaning. Some of these synonyms include "concentrated on," "engrossed in," "immersed in," "entranced by," "captivated by," "enchanted by," "mesmerized by," "riveted by," and "absorbed in." These synonyms can be used in different contexts, whether it be in a professional or personal setting, to indicate one's interest or concentration towards a task or person. With the use of synonyms, one can add variety and depth to their vocabulary, making their communication more effective and engaging.