D-Day
Allied casualties were much lighter than feared - just 2500 were killed on 'D-Day', 6 June 1944. For one thing, the Germans were taken by surprise. They did not expect a landing in Normandy since they could not see how any troops could be kept supplied. Secondly, Hitler was convinced that the Normandy landings were not the real invasion and so he kept vital troops back in reserve, waiting for the 'real' attack to take place. This allowed the Allied troops to establish themselves on French soil. Thirdly, the Allies had total control of the skies and used this to bomb bridges and roads to stop the Germans bringing up reinforcements to the Normandy area.
The German infantry were bitter about the failure of the German Air Force to challenge the Allied aircraft. A popular German infantry joke of the time went like this: 'If the plane shows up dark in the sky, it's the RAF. If it shows up silvery, it's the US Air Force and if it doesn't show up at all, it's one of ours!'
Neil Demarco: The era of the Second World War; Oxford University Press, 1993/2000, page 45