How to write an i-breve (an i with a breve accent, but without the dot)

The dotless i is \i; so you would want \u{\i}. (A dotless j is, likewise, \j).

Use math simbols:

\breve{\imath}

Or

\breve{\jmath}

\breve is the accent and \imath / \jmath are i / j without the upper dot