There is no conventional way.
However, you can use VNC (the open source screen sharing protocol) and this clever program (below) to make the iMac G4
pretend to be an external
second display. The Mac mini needs to have a display connected the usual way as the primary display. The program is ScreenRecycler.
http://www.screenrecycler.com/home.html
You run ScreenRecycler on the Mac mini. It sets up a second virtual screen that acts like a real external display and
shares that screen over the network. It's like a Mac doing screen sharing (for remote control from another computer), except the screen being shared is this second virtual screen, not the primary screen.
Then, you run a VNC client program (such as the developer's own freeware JollysfastVNC) on the iMac G4 to display that shared screen in a window. When you go +full screen+ with that window, the iMac display appears to be the Mac mini's second display.
The signal is going over the network, so you are not going to get blazing speed. But since the iMac has decent 100Base-T wired networking (and the Mac mini has gigabit Ethernet), as long as you use a good Cat-5 rated Ethernet cable or better, it should be reasonably fast. The program is not free, but you can try it in limited-time demo mode for free, to see if it is suitable.
I use it to give my Intel iMac a
third display (the first two connected the usual way). The ScreenRecycler screen is an old PC laptop running Linux (Ubuntu).