The pilot reported that he was approaching the airport with the intention of performing three touch and go landings. He went over the landing checklist as he was nearing the field, but he did not put the landing gear down because he was not on the downwind leg, where he would normally complete the checklist. He reported, “As I turned final, I thought I had the gear down but didn’t.” He reported that the gear up warning horn never sounded. The airplane touched down in a wings level attitude on the runway, which resulted in a bent propeller and substantial damage to the “hat” assemblies, which are U-shaped structural channels on the belly of the airplane. The landing gear handle was found in the UP position. The inspection of the airplane revealed that the landing gear extended and retracted when the airplane was put on jacks. The “Warning Gear Unsafe” light illuminated when the throttle was pulled to the idle position with the landing gear in the retracted position. The “Warning Gear Unsafe” light is about a 1-inch square red light located directly in front of the pilot on the instrument panel. However, the “Gear Warning Horn” did not sound.