German shares recorded small gains at the start of trading on Tuesday, with the benchmark DAX index rising 45.11 points, or 0.28 percent, opening at 15,897.9 points. The biggest winner among Germany’s 30 largest listed companies was online food delivery company Delivery Hero, increasing by 2.85 percent, followed by carmaker Volkswagen with 2.25 percent and plastic specialist Covestro with 1.93 percent. Shares of Vonovia fell by 2.45 percent. The German housing company was the biggest loser at the start of trading on Tuesday after making a third and final takeover offer for its national competitor Deutsche Wohnen on Monday. German gross domestic product (GDP) in the second quarter of 2021 rose by 1.6 percent on the previous quarter after adjustment for price, seasonal and calendar variation. GDP was even up 9.4 percent year-on-year, the Federal Statistical Office (Destatis) announced on Tuesday.