1080p can be any refresh rate. We're used to 60Hz because that's what our TV's operate at. Our TV's are that way because our electrical service operates at in North America. In Europe, electricity is distributed at 50Hz, which is why PAL video is based on 50Hz refresh rates. Film is shot and projected at 24 frames per second. HD-DVD and Blu-ray video is being encoded at 1080p/24, if I remember correctly, although players that support output at 1080p/24 have been hard to find (if they offer 1080p, they generally force a 3-2 pulldown to get the video to 1080p/60). You may be hard pressed to find a source that will provide 1080p/24.

What projector are you using?