Bulletin of the American Mathematical Society

Author(s): 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 Grassmann structures, Soviet Math. Dokl. 21 (1980), no. 3. Further references to works by V. Goldberg and other Soviet mathematicians on the subject can be found in this paper. 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.
12.: B. Saint-Donat, Variétés de translation et théorème de Torelli, Comptes Rendus Paris 280 (1975), 1611-1612. 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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