One year after returning from Spain, in 1926, Geiger attended Eduard Pfeiffer's architectural class at the Kunstgewerbeschule in Munich. He graduated as an architect in 1935 and spent half a year in Rome together with his father. Geiger then worked in a Munich architect's bureau until 1940 when he was sent to the Russian Front. Typical of this period are his dark-coloured landscapes in watercolour. Geiger returned to Germany for a short period in 1942 before his father helped him to get a job as a war painter in the Ukraine. Geiger returned to Munich after the end of the war. His first abstract work was exhibited in 1948 at the 'Salon des Réalités Nouvelles' in Paris.
One year later he joined up with Baumeister, Matschinsky-Denninghoff and Winter and founded the group 'ZEN 49'. Geiger discovered his true style during the 1950s. He integrated the futurist style of the Sixties, which was influenced by space research, into his abstract and colourful compositions. He repeatedly showed works at the documenta in Kassel between 1959 and 1977. He gave up working as an architect in 1962 in order to concentrate on his painting. In 1965 he was appointed professor at the Akademie in Düsseldorf, a post that he held until 1976. Geiger's typical works from the middle of the 1970s are rectangular or oval shapes, preferably in synthetic shades of red paint, which he sprayed onto the canvas. Geiger has been a member of the Akademie der Schönen Künste in Munich since 1982. In 1987 he was commissioned with the sculpture 'Gerundetes Blau' for the cultural centre Gasteig in Munich. At present Geiger lives and works in Munich. His abstract colour compositions make him one of the most important artists of 'Farbfeldmalerei' (colour field painting) in Germany.