  erich kÃ¤hler (; 16 january 1906, leipzig &ndash; 31 may 2000, wedel) was a german mathematician with wide-ranging geometrical interests. ==education and career== kÃ¤hler was born in leipzig, and studied there. he received his ph.d. in 1928 from the university of leipzig. he held professorial positions in kÃ¶nigsberg, leipzig, berlin and hamburg. later in life he became interested in general philosophical issues. ==contributions== as a mathematician he is known for a number of contributions: the cartan&ndash;kÃ¤hler theorem on singular solutions of non-linear analytic differential systems; the idea of a kÃ¤hler metric on complex manifolds; and the kÃ¤hler 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 kÃ¤hler counts as a major developer of the theory from its formal genesis with Ãlie cartan. kÃ¤hler manifolds &mdash; complex manifolds endowed with a riemannian metric and a symplectic form so that the three structures are mutually compatible &mdash; are named after him. the k3 surface is named after kummer, kÃ¤hler, 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. ==see also== *almost complex manifold *hyper-kÃ¤hler manifold *kÃ¤hler&ndash;einstein metric *quaternion-kÃ¤hler manifold *complex poisson manifold *special kÃ¤hler geometry ==references== * kÃhler, erich ernst international who's who. accessed september 3, 2006. *    
1906_births 2000_deaths 20th-century_mathematicians Algebraic_geometers German_mathematicians Leipzig_University_alumni Leipzig_University_faculty People_from_Leipzig People_from_the_Kingdom_of_Saxony University_of_KAPnigsberg_alumni