Friday, December 17, 2004

RIP: Shiing-shen Chern (1911-2004)

Shiing-shen Chern was a Chinese mathematician, who was one of the leading differential geometers of the twentieth century.

"Chern's work spreads over all the classic fields of differential geometry. It includes areas currently fashionable (the Chern-Simons theory arising from a joint paper in 1974), perennial (the Chern-Weil theory linking curvature invariants to characteristic classes from 1944, after the Allendoerfer-Weil paper of 1943 on the Gauss-Bonnet theorem), the quotidian (Chern classes), and some areas such as projective differential geometry and webs that have a lower profile. He published results in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.

He was a true follower of √Člie Cartan, working intensely on the 'theory of equivalence' in his time in China from 1937-1943, in relative isolation. In 1954 he published his own treatment of the pseudogroup problem that is in effect the touchstone of Cartan's geometric theory. He used the moving frame method with success only matched by its inventor; he preferred in complex manifold theory to stay with the geometry, rather than follow the potential theory. In his contribution to the IMU Millennium volume, Chern proposed that Finsler metrics would be important to the mathematics of the twenty-first century."

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