The pilot of the retractable-landing gear equipped-airplane reported that, while in the traffic pattern, he was distracted while looking for other aircraft and failed to continue the landing checklist, but he assumed it was completed. During the approach, he reduced power and did not hear the landing gear warning horn. The pilot then landed the airplane with the landing gear retracted. The pilot added that, during the recovery process with a tow truck, they attempted to troubleshoot the landing gear warning system, but they still did not hear the landing gear warning horn. The airplane sustained substantial damage to the left wing. Postaccident examination by a Federal Aviation Administrator inspector revealed that the landing gear audible warning horn switch on the bulkhead (engine compartment) was improperly rigged, and the horn did not sound when tested. He added that the airplane was equipped with a mirror on the right wing, which the pilot could have used to visually check if the landing gear were extended.