The pilot reported that he entered the airport traffic pattern after a local sightseeing flight and began the before landing checklist. Three other aircraft announced their presence in the vicinity of the airport and the pilot turned his attention to locating the other aircraft without finishing the checklist. The pilot reported that he did not hear the gear warning horn annunciate while he was wearing his noise cancelling headset and landed with the gear retracted. A postaccident examination revealed substantial damage to the fuselage supporting structure. After the accident, the airplane was put on jack stands and the landing gear was extended manually. The landing gear was not operated through the use of the airplane's electrical system. The pilot reported flying the airplane the previous day and the landing gear operated normally. The pilot reported no preimpact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.