Rittmann left Geneva to study with Alfred Lacroix in Paris, Friedrich Johann Karl Becke in Vienna, Ernst Anton Wülfing and Victor Mordechai Goldschmidt in Heidelberg.
At the annual meeting of the German Geological Society in January 1939, he was right opposing the idea that the Mid-Atlantic Ridge was an orogenic uplift by compression, and his opposition to disregard the Continental drift theory raised doubts.
The work "Über den Zustand des Erdinnern und seine Entstehung aus einem homogenen Urzustand" (Kuhn and Rittmann, 1941) defended the non existence of an iron-nickel Earth core.
His work "Orogénèse et volcanisme" (Rittmann, 1951) with collaboration of W. Kuhn demonstrated that crystalline mantle is able to creep under its pressure and temperature.
For similar reasons, it was suspected the existence of drowned mountains transverse to the Ridge that connect North Africa to Central America.