what's the minimum depth of a wire channel in a concrete ceiling?
If you cut a "trench" in a concrete ceiling, you potentially weaken the strength of the structure. Not a good idea. Better to use already available surface mount wiring channel (trade name "Wiremold" for reference only) and if it bothers you, change your attitude about it. Or hide it beneath some architecturally unnecessary structure, like a faux beam made of stryrofoam and painted to look like the concrete (people sell this for that exact reason). Compromising safety for aesthetics is never a great plan.