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Web geometry. (English) Zbl 0483.53013

MSC:
53A60 Differential geometry of webs
14C21 Pencils, nets, webs in algebraic geometry
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
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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. · Zbl 0516.53012
[2] W. Blaschke and G. Bol, Geometrie der Gewebe, Springer, Berlin, 1938. · JFM 64.0727.03
[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. · Zbl 0386.14002
[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. · Zbl 0402.57001
[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. · Zbl 0339.14003
[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. · JFM 14.0642.01
[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. · JFM 26.0510.01
[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. · JFM 32.0459.04
[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). · Zbl 0304.14022
[13] N. Tschebotarow, Über Flächen welche Imprimitivitätssysteme in Bezug auf eine gegebene Kontinuirliche Transformationsgruppe enthalten, Recueil Math. (Sbornik) 34 (1927), 149-204. · JFM 53.0397.02
[14] W. Wirtinger, Lies Translationsmannigfaltigkeiten und Abelsche Integrale, Monatshefte Math. Phys. 46 (1938), 384-431. · Zbl 0019.18204
[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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