On May 29, 2018, about 1345 eastern daylight time, a Cessna 337E, N86507, was substantially damaged during a gear-up landing at the DeKalb-Peachtree Airport (PDK), Atlanta, Georgia. The private pilot and the passenger were not injured. The airplane was co-owned and operated by the pilot as a Title 14 Code of Federal Regulations Part 91 personal flight. Visual meteorological conditions prevailed, and no flight plan was filed for the flight that departed North Perry Airport (HWO), Hollywood, Florida, about 0945.The pilot stated that he was unable to extend the landing gear while on approach to the airport. He declared an emergency and flew north of the airport where he attempted to pump the landing gear down via the emergency gear-extension handle. The pilot was unable to pump the gear down and observed a large puddle of red hydraulic fluid on the floorboards near the hydraulic pump. The pilot realized that he would not be able to extend the gear and made a gear-up landing on runway 21R, which resulted in substantial damage to the lower fuselage. A postaccident examination of the airplane revealed that when the emergency hydraulic pump actuator, located between the cockpit seats, was activated very little hydraulic resistance was noted when the emergency gear-extension handle was pumped. The hydraulic reservoir was nearly depleted. Further examination revealed that, as the emergency handle was activated, a stream of hydraulic fluid sprayed from the surface of the aluminum line connecting the emergency handle/pump to the electric hydraulic pump that was mounted under and behind the instrument panel of the pilot's side. The line was about 23 inches long. The plastic sheathing protecting the line was intact and removed to facilitate examination of the leaking area. There were no areas of line chafing noted on the line and no adjacent structure where chafing would occur. The leaking hydraulic line was removed and examined. A visual examination using 10x magnification revealed an area of corrosion and pitting on the aluminum surface. The affected area was about 0.75 inches long and covered about half the circumference of the tube. The pilot held a private pilot certificate with a rating for airplane single-engine land. His last Federal Aviation Administration (FAA) second-class medical was issued on December 12, 2017. Weather reported at the airport at 1359 included wind from 140° at 9 knots, visibility 10 miles, few clouds at 3,800 ft, scattered clouds at 4,900 ft, broken clouds at 6,000 ft, temperature 26° C, dew point 22° C, and an altimeter setting of 29.82 inHg.