I Want To Move A Ceiling Light Over About Ten Inches Without Moving The Existing Electrical Box. How Would I Do That?

You can install a new box to mount the light on, then extend the wire from the old box to the new box, and install a blank cover on the old box.  At bare minimum, the new light has to be mounted on a box, and the old box connections have to be accessible.
TURN OFF POWER BEFORE ATTEMPTING WIRING.