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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
DOI: https://doi.org/10.1090/S0273-0979-1982-14955-2
MathSciNet review: 634430
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  • 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
  • 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.
  • 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 469925
  • 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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