The pilot reported that he was receiving instruction in an airplane with retractable landing gear. He further reported that during landing, the airplane touched down and began sliding on the concrete runway, and he "knew something was wrong". The flight instructor reported that he was the pilot in command of the airplane and that on final both pilots were on the controls. He further reported that he realized there was an issue when he heard metal on pavement. The airplane impacted the runway with its landing gear retracted, causing substantial damage to the fuselage and bulkhead. The pilot receiving instruction reported that there were no pre impact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation. There was a post-accident landing gear aural warning horn check/test conducted, with no maintenance issues found.