Surface Theory with Darboux and Bianchi

  • Shiing-Shen Chern


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.


Minimal Surface Principal Curvature Surface Theory Asymptotic Curve Focal Surface 
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  1. 1.
    Bryant, R., Chern, S., Griffiths, P.A. (1990): Exterior differential systems. Proc. of 1980 Beijing DD-Symposium (1980), 219–338 or Bryant-Chern- Gardner-Goldschmidt-Grifliths, Exterior Differential Systems, SpringerGoogle Scholar
  2. 2.
    Chern, S. (1989): Deformation of surfaces preserving principal curvatures. Differential geometry and complex analysis, volume in memory of H. Rauch. Springer, 1984, pp. 155–163, or Chern, selected papers, vol. 4, pp. 95–103, SpringerGoogle Scholar
  3. 3.
    Chern, S., Wolfson, J. (1989): Harmonic maps of the two-sphere into a complex Grassmann manifold, II. Annals of Mathematics 125 (1987) 301–335 or S. Chern, selected papers, vol. 4, p. 189–223, SpringerGoogle Scholar
  4. 4.
    Hopf, H. (1983): Differential geometry in the large, part. II. Lecture notes in mathematics, vol. 1000. SpringerMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1991

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  • Shiing-Shen Chern

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