nLab Shiing-Shen Chern

• Wikipedia entry

Selected writings

On Euler forms and the Gauss-Bonnet theorem:

• Shiing-Shen Chern, A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds, Annals of Mathematics Second Series, Vol. 45, No. 4 (1944), pp. 747-752 (jstor:1969302)

On principal bundles, their characteristic classes and introducing the Chern-Weil homomorphism:

• Shiing-Shen Chern, Differential geometry of fiber bundles, in: Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, pages 397-411, Amer. Math. Soc., Providence, R. I. (1952) (pdf, full proceedings vol 2 pdf)

Introducing Chern-Simons forms:

• Shiing-Shen Chern, James Simons, Section 2 of: Characteristic Forms and Geometric Invariants, Annals of Mathematics Second Series, Vol. 99, No. 1 (Jan., 1974), pp. 48-69 (jstor:1971013)

Quotes

Chen Ning Yang writes in C. N. Yang, Selected papers, 1945-1980, with commentary, W. H. Freeman and Company, San Francisco, 1983, on p. 567,

recalled in: D. Z. Zhang, C. N. Yang and contemporary mathematics The Mathematical Intelligencer 15, 13–21 (1993) (doi:10.1007/BF03024319):

In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”

Related entries

• Chern class

• Euler form

• Chern-Weil theory

  • Chern-Weil homomorphism

  • Gauss-Bonnet theorem

  • Chern-Gauss-Bonnet theorem

• secondary characteristic class

  • Chern-Simons form

• CR manifold

category: people