Shiing-Shen Chern

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Shiing-Shen Chern in Oberwolfach , 1976

Shiing-Shen Chern ( Chinese  陳省身  /  陈省身 , Pinyin Chén Xǐngshēn , IPA ( standard Chinese) [ tʂʰən.ɕiŋ.ʂən ], GR Chern Shiing-Shen ; born October 28, 1911 in Jiaxing , Empire of China , † December 3, 2004 in Tianjin , China ) was a Chinese and American mathematician whose work played a leading role in the field of differential geometry .

life and work

He was born at the end of the Qing Dynasty in Jiaxing, Zhejiang Province , and moved to live with his father in Tianjin in 1922 . In 1926 he began to study at Nankai University in Tianjing. 1930-1934 he studied under Dan Sun at Tsinghua University . He impressed the differential geometer Wilhelm Blaschke , who was then leading with Élie Cartan, during a visit to this university in 1932 and received a scholarship in 1934 to study with him in Hamburg .

Reprint of his doctoral thesis in Hamburg (1936)

In 1936 he received his doctorate and then went to Élie Cartan in Paris, after which he returned to China. His university was moved to Kunming during the Japanese occupation . In 1943 he went to Princeton to the Institute for Advanced Study , where he impressed Hermann Weyl , Oswald Veblen and Solomon Lefschetz . The latter made him an editor of the Annals of Mathematics, which he directed . In 1946 he founded the Mathematics Institute of the Chinese Academy in Shanghai . In 1948 he was back in Princeton because of the civil war in China, and then in 1949 he became professor in Chicago . In 1960 he went to Berkeley and became a US citizen a year later. In 1981 he founded the Mathematical Sciences Research Institute (MSRI) in Berkeley , of which he was director until 1984. In 1985 he founded the Nankai Institute of Mathematics in Tianjin, which he headed until his death.

After preliminary work by André Weil , Carl B. Allendoerfer a . a. in the 1940s the Gauss-Bonnet theorem of differential geometry with the topology of the underlying manifolds and generally investigated the relationship between curvature and topology ( Chern-Weil theory ), which he investigated with the geometry of fiber bundles. The Chern classes (special characteristic classes of complex vector bundles) and the Chern-Simons theory (from a work with James Simons in 1974), which also has many applications in physics, since the invariant form of a Yang mill described in it, are named after him Gauge theory serves as an active functional of a topological quantum field theory. He also worked on the differential geometry of complex manifolds , Finsler spaces , minimal submanifolds , projective differential geometry , integral geometry, geometry of tissues (many of the fields of work of his teacher Wilhelm Blaschke ) and the like. a.

Most recently he dealt with the old problem of the existence of complex structures on the 6-sphere, open since 1953, whereby he introduced new aspects (exceptional Lie group G2 and Yang-Mills theory techniques), but his first proof of non-existence was sketchy. He then worked on an improvement until his death.

He had been married since 1939 and had a son Paul and a daughter May Chu (married to the physicist Paul Chu ).

His PhD students include Shing-Tung Yau , Katsumi Nomizu , Louis Auslander , Alan Weinstein , Joseph A. Wolf , Haruo Suzuki , Robert Brown Gardner , Manfredo do Carmo , Thomas Banchoff , David Bleecker , Howard Garland .


In 1984 he received the Wolf Prize , in 1983 the Leroy P. Steele Prize of the American Mathematical Society . In 2004 he was honored with the Shaw Prize . In 1970 he gave a plenary lecture at the ICM in Nice ( Differential Geometry: its past and its future ) and also in 1950 in Cambridge (Massachusetts) (The differential geometry of fiber bundles). In 1958 he was invited speaker at the International Congress of Mathematicians in Edinburgh (Differential geometry and integral geometry). In 1970 he received the Chauvenet Prize , the National Medal of Science in 1975 , the Lobatschewski Medal in 2002 and the Humboldt Research Prize in 1982.

He was a member of the Academia Sinica , the National Academy of Sciences (1961), the American Academy of Arts and Sciences (1963), the Royal Society (1985), the Académie des sciences (1989), the American Philosophical Society (1989), the Russian Academy of Sciences (1999), the Brazilian and Chinese Academy of Sciences , the Accademia dei Lincei and honorary member of the London Mathematical Society . He has received several honorary doctorates, including from the TU Berlin, the University of Chicago, the University of Hamburg (1971), the University of Hong Kong, SUNY and the ETH Zurich .

Since 2010 the International Mathematical Congresses awarded Chern Medal is named in his honor. It is endowed with $ 250,000 for the awardee and another $ 250,000 for research funding. There is also the Chern Prize , which has been awarded every three years since 2001 to mathematicians of Chinese origin at the International Congress of Chinese Mathematicians (ICCM).

Publications (selection)

  • A mathematician and his mathematical work. Selected papers of SS Chern (Eds. SY Cheng, P. Li, G. Tian), World Scientific 1996, also 2 vols. 1978, 1989 (with prefaces by Griffiths and Weil)
  • Complex manifolds without potential theory , Springer 2nd edition 1979 (first 1967)
  • Lectures on differential geometry , world scientific 1999
  • Riemann-Finsler geometry , world scientific 2005
  • with Robert Bryant, Hubert Goldschmidt, Robert Gardner, Phillip Griffiths Exterior differential systems , Springer 1991
  • Global differential geometry , MAA (Mathematical Association of America) 1989
  • From triangles to manifolds , American Mathematical Monthly, May 1979
  • What is geometry? , American Mathematical Monthly, October 1990
  • Differential geometry - its past and its future , ICM 1970 (International congress mathematicians)
  • Differential geometry of fiber bundles , ICM 1950
  • Characteristic classes of Hermitean manifolds , Annals of Mathematics 47, 1946, p. 85 (Chernklassen)
  • with James Simons Characteristic classes and geometric invariants , Annals of Mathematics 99, 1974, p. 48 (Chern-Simons Invariante)
  • A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds , Annals of Mathematics 45, 1944, pp. 747-752
  • Some new viewpoints of differential geometry in the large , Bulletin American Mathematical Society 42, 1946, pp. 1-30
  • Curves and surfaces in euclidean space , Studies in global geometry and analysis 1967 (won the Chauvenet Prize)


  • P. Griffiths, André Weil , Yang, Yau, Wilhelm Klingenberg a . a .: Chern - a great geometer of the 20th century , Hong Kong 1992
    • therein by: Richard Palais , Chuu-Lian Terng : The life and mathematics of Shiing-Shen Chern (also reprinted in Chen, Li, Tiang, Selected Papers of SS Chern, World Scientific 1996, pp. 1–42, together with Chern, My mathematical education, Chern, A summary of my scientific life and works, A. Weil, SS Chern as Geometer and Friend, Griffiths, Some reflections on the mathematical contribution of SS Chern, WL Chow, Shiing-Shen Chern as friend and mathematician)
  • Albers, Alexanderson Mathematical people , AMS 1985

Web links

Individual evidence

  1. October 28 to RS Palais, C.-L. Terng, The life and mathematics of Shiing-Shen Chern, in: Cheng, Li, Tian, ​​A mathematician and his mathematical work. Selected Papers of SS Chern, World Scientific 1996, p. 2, and the Curriculum Vitae printed there, p. 695. In the obituary by H. Wu, Bull. AMS 2009, Hitchin, Bulletin London Math. Soc. 2006, is stated October 26th.
  2. Robert Bryant , S.-S. Chern's study of almost-complex structures on the six-sphere, Arxiv 2014
  3. Mathematics Genealogy Projec