The pilot performed a landing with the landing gear in the retracted position. While the airplane was on the base leg of the traffic pattern, the pilot heard a helicopter pilot make a transmission over the common radio frequency. The approach checklist was complete and the copilot called for the landing gear to be extended. The pilot thought that he lowered the gear while searching for the helicopter he knew was in the vicinity. On final approach the airplane was configured with full flaps and the pilot announced that the before landing checklist was complete; he had no recollection of visually observing the landing gear lights illuminate green. Upon landing flare, he realized something was amiss and looked down at the instrument panel. He saw that the landing gear lights were illuminated red and reached to the gear handle to verify it was in the down position. The airplane made a smooth touchdown with the landing gear in the retracted position. The pilot stated that he did not make the proper check for the gear extension due to the timing of the helicopter distraction. The pilot reported no preimpact mechanical malfunctions or failures with the airplane or engine, stating that the accident was the result of pilot error. The airplane incurred thermal damage to the wing structure. The pilot further stated that there were no audible warning indications that the landing gear were retracted.