Kähler was born in Leipzig, and studied there. He received his Ph.D. in 1928 from the University of Leipzig. He held professorial positions in Königsberg, Leipzig, Berlin and Hamburg. Later in life he became interested in general philosophical issues.
As a mathematician he is known for a number of contributions: the Cartan-Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Élie Cartan.
Kähler manifolds — complex manifolds endowed with a Riemannian metric and a symplectic form so that the three structures are mutually compatible — are named after him.
The K3 surface is named after Kummer, Kähler, and Kodaira.
His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted.
* KÄHLER, Erich Ernst International Who's Who. accessed September 3, 2006.
* Erich Kähler at the Mathematics Genealogy Project