Web geometry
Shiing-Shen Chern
Source: Bull. Amer. Math. Soc. (N.S.) Volume 6, Number 1
(1982), 1-8.
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Permanent link to this document: http://projecteuclid.org/euclid.bams/1183548587
Mathematical Reviews number (MathSciNet): MR634430
Zentralblatt MATH identifier: 0483.53013
References
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.
Zentralblatt MATH: 0516.53013
Mathematical Reviews (MathSciNet): MR706902
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.
Zentralblatt MATH: 0474.14003
Mathematical Reviews (MathSciNet): MR494957
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.
Zentralblatt MATH: 0402.57001
Mathematical Reviews (MathSciNet): MR507000
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.
Zentralblatt MATH: 0339.14003
Mathematical Reviews (MathSciNet): MR435074
Digital Object Identifier: doi:10.1007/BF01390145
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.
Mathematical Reviews (MathSciNet): MR1504382
12. B. Saint-Donat, Variétés de translation et théorème de Torelli, Comptes Rendus Paris 280 (1975), 1611-1612.
Zentralblatt MATH: 0304.14022
Mathematical Reviews (MathSciNet): MR469925
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.
Zentralblatt MATH: 0019.18204
15. David B.. Damiano, Webs, abelian equations, and characteristic classes, Thesis, Brown University, 1980.
Mathematical Reviews (MathSciNet): MR2631141
16. John B. Little, Translation manifolds and the converse of Abel's theorem, Thesis, Yale University, 1980.
Zentralblatt MATH: 0521.14017
Bulletin (New Series) of the American Mathematical Society
