Shiing-Shen Chern

Quotes

• “In 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature.”
• “Integral geometry, started by the English geometer M. W. Crofton, has received recently important developments through the works of W. Blaschke, L. A. Santaló, and others. Generally speaking, its principal aim is to study the relations between the measures which can be attached to a given variety.”
• “Not all the geometrical structures are "equal". It would seem that the riemannian and complex structures, with their contacts with other fields of mathematics and with their richness in results, should occupy a central position in differential geometry. A unifying idea is the notion of a G-structure, which is the modern version of an equivalence problem first emphasized and exploited in its various special cases by Elie Cartan.”
• “The main object of study in differential geometry is, at least for the moment, the differential manifolds, structures on the manifolds (Riemannian, complex, or other), and their admissible mappings. On a manifold the coordinates are valid only locally and do not have a geometric meaning themselves.”
• “The treatises of Darboux (1842–1917) and Bianchi (1856–1928) on surface theory are among the great works in the mathematical literature. They are: G. Darboux, Théorie générale des surfaces, Tome 1 (1887), 2 (1888), 3 (1894), 4 (1896), and later editions and reprints. L. Bianchi. Lezioni di Geometria Differenziale, Pisa 1894; German translation by Lukat, Lehrbuch der Differentialgeometrie, 1899. The subject is basically local surface theory.”

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Key facts

Born

( 1911-10-26 ) October 26, 1911 , Jiaxing , Zhejiang, Qing China

Died

December 3, 2004 (2004-12-03) (aged 93), Tianjin , China

Citizenship

United States

Education

Nankai University ( BS ), University of Hamburg ( PhD )

Known for

Chern class , Chern–Gauss–Bonnet theorem , Chern–Simons theory , Chern–Simons form , Chern–Weil theory , Chern–Weil homomorphism , Chern's conjecture , Chern's conjecture (differential geometry) , Bott–Chern cohomology , Chern–Bott formula, Chern–Lashof theory

Awards

Chauvenet Prize (1970) National Medal of Science (1975) Wolf Prize (1983) Lobachevsky Medal (2002) Shaw Prize (2004) ForMemRS (1985)

Fields

Mathematics

Institutions

Tsinghua University , Institute for Advanced Study , University of Chicago , University of California, Berkeley , Mathematical Sciences Research Institute , Nankai University , Chern Institute of Mathematics

Thesis

Eine Invariantentheorie der Dreigewebe aus r-dimensionalen Mannigfaltigkeiten im R 2 r {\displaystyle R_{2r}}

Doctoral advisor

Wilhelm Blaschke

Other notable students

James Simons , Chen Ning Yang

Traditional chinese

陳省身

Simplified chinese

陈省身

Hanyu pinyin

Chén Xǐngshēn

Bopomofo

ㄔㄣˊ ㄒㄧㄥˇ ㄕㄣ

Gwoyeu romatzyh

Chern Shiing-Shen

Wade giles

Ch'en Hsing-shen

via Wikipedia infobox

Wikidata facts

Image

Shiing-shen Chern 1988 (re-scanned) (cropped-1).jpg

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