The pilot arrived at his destination and joined the circuit. The downwind checks were completed without interruption and the pilot reported that he observed three green gear down lights. The final approach was normal except for a flickering of the alternator warning light during the flare. The pilot completed a "PUF" check on final approach and reported that he again observed three green lights. The aircraft touched down smoothly on the flaps, then the undersurface of the fuselage. Neither the pilot nor the passenger heard the gear warning horn. The gear selector was found to be in the gear down position and the gear actuator circuit breaker had popped. The main gear doors were found to be partly open as if the gear down cycle had started, however, it was reported that there were no scrape marks on the doors to indicate that they had dragged along the strip during the ground slide. The pilot stated that he did not select gear down after the aircraft had landed. During gear retraction and extension checks after the accident the gear was found to work normally, although the gear warning horn worked only intermittently. At the time the pilot flew the downwind leg of the circuit the sun would have been shining onto the instrument panel. It is likely that the gear down lights were illuminated by the sun which would have made it difficult for the pilot to see if there was a gear down indication. Having assumed that the gear down lights were on, he probably formed a false hypothesis that they were indeed on and did not check the gear position indicator thoroughly during his "PUF" check. When the warning horn failed to activate during the flare the last chance to avoid an accident was lost and the aircraft landed with the gear retracted. How the gear selector got into the gear down position is open to conjecture. This accident was not the subject of an on-site investigation.