Lastly I updated Google Earth to the latest version and after I started it I saw the following:
After searching the Internet I found the page of Google where they give some points which should be checked; such as: install the latest display driver, ...
But I already had the latest drivers.
While browsing trough the options of Google Earth I found that the display mode can be changed. After changing it to DirectX it worked correctly.
To change the setting:
1. go to the options
2. And then change the graphics mode to DirectX