Which of the following extraocular eye muscles is not innervated by the oculomotor nerve?

The extraocular eye muscle that is not innervated by the oculomotor nerve (cranial nerve III) is the lateral rectus muscle. This muscle is innervated by the abducens nerve (cranial nerve VI).

To clarify, the oculomotor nerve innervates most of the extraocular muscles, including:

1. Superior rectus
2. Medial rectus
3. Inferior rectus
4. Inferior oblique

However, the lateral rectus muscle, which abducts the eye, and the superior oblique muscle (innervated by the trochlear nerve, cranial nerve IV) are exceptions to this rule.

Thus, in summary, the lateral rectus muscle is not innervated by the oculomotor nerve; rather, it is controlled by the abducens nerve.