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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Web geometry


Author: Shiing-Shen Chern
Journal: Bull. Amer. Math. Soc. 6 (1982), 1-8
MSC (1980): Primary 53A60, 14D25
MathSciNet review: 634430
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  • 1. M. A. Akivis, Webs and almost Grassmannian structures, Differential geometry (Budapest, 1979) Colloq. Math. Soc. János Bolyai, vol. 31, North-Holland, Amsterdam-New York, 1982, pp. 23–40. MR 706902 (84m:53024)
  • 2. W. Blaschke and G. Bol, Geometrie der Gewebe, Springer, Berlin, 1938.
  • 3. S. S. Chern and P. A. Griffiths, Abel's theorem and webs, Jahresberichte der deut. Math. Ver. 80 (1978), 13—110; also, Corrections and Addenda, same Journal, 83 (1981), 78—83.
  • 4. S. S. Chern and P. A. Griffiths, An inequality for the rank of a web and webs of maximum rank, Ann. Scuola Norm. Pisa, Serie IV, 5 (1978), 539—557.
  • 5. G. Darboux, Théorie des surfaces, t.1, (1914), 151—161.
  • 6. P. A. Griffiths, Variations on a theorem of Abel, Invent. Math. 35 (1976), 321—390.
  • 7. S. Lie, Bestimmung aller Flächen, die in mehrfacher Weise durch Translationsbewegung einer Kurve erzeugt werden, Arch. für Math. Bd. 7, Heft 2 (1882), 155—176; also Ges. Abhandlungen, Bd. 1, Abt 1, 450—467.
  • 8. S. Lie, Das Abelsche Theorem und die Translationsmannigfaltigkeiten, Leipziger Berichte 1897, pp. 181—248; also Ges. Abhandlungen, Bd. II, Teil II, paper XIV, pp. 580—639.
  • 9. S. Lie, Ges. Abhandlungen, Bd. 7.
  • 10. H. Poincaré, Fonctions abeliennes, J. Math. Pures Appl., Serie 5, t.1, (1895), 219—314; also Oeuvres t.IV, pp. 384—472, in particular p. 430.
  • 11. H. Poincaré, Sur les surfaces de translation et les fonctions abeliennes, Bull. Soc. Math. France 29 (1901), 61—86; also Oeuvres t.VI, pp. 13—37.
  • 12. Bernard Saint-Donat, Variétés de translation et théorème de Torelli, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), no. 23, Aii, A1611–A1612 (French, with English summary). MR 0469925 (57 #9705)
  • 13. N. Tschebotarow, Über Flächen welche Imprimitivitätssysteme in Bezug auf eine gegebene Kontinuirliche Transformationsgruppe enthalten, Recueil Math. (Sbornik) 34 (1927), 149-204.
  • 14. W. Wirtinger, Lies Translationsmannigfaltigkeiten und Abelsche Integrale, Monatshefte Math. Phys. 46 (1938), 384-431.
  • 15. David B.. Damiano, Webs, abelian equations, and characteristic classes, Thesis, Brown University, 1980.
  • 16. John B. Little, Translation manifolds and the converse of Abel's theorem, Thesis, Yale University, 1980.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1982-14955-2
PII: S 0273-0979(1982)14955-2