Geodesic
Abelian equations and rank problems for planar webs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2007), pp. 40-75.

Voir la notice de l'article provenant de la source Math-Net.Ru

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V. V. Goldberg; V. V. Lychagin. Abelian equations and rank problems for planar webs. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2007), pp. 40-75. http://geodesic.mathdoc.fr/item/IVM_2007_10_a2/

[1] Bol G., “On $n$-webs of curves in a plane”, Bull. Amer. Math. Soc., 38 (1932), 855–857 | DOI | MR

[2] Blaschke W., Bol G., Geometrie der Gewebe, Springer-Verlag, Berlin, 1938, viii+339 pp.

[3] Blaschke W., Einführung in die Geometrie der Waben, Birkhäuser-Verlag, Basel–Stutgart, 1955, 108 pp. | MR | Zbl

[4] Chern S. S., “Web geometry”, Bull. Amer. Math. Soc. (N.S.), 6:1 (1982), 1–8 | DOI | MR | Zbl

[5] Dou A., “Plane four-webs”, Mem. Real Acad. Ci. Art. Barcelona, 31:5 (1953), 133–218 | MR

[6] Dou A., “Rang der ebenen $4$-Gewebe”, Abh. Math. Sem. Univ. Hamburg, 19:3/4 (1955), 149–157 | DOI | MR | Zbl

[7] Pantazi Al., “Sur la détermination du rang d'un tissu plan”, C. R. Inst. Sci. Roum., 2 (1938), 108–111

[8] Pantazi Al., “Sur une classification nouvelle des tissus plans”, C. R. Inst. Sci. Roum., 4 (1940), 230–232

[9] Mihăileanu N. N., “Sur les tissus plans de première espèce”, Bull. Math. Soc. Roum. Sci., 43 (1941), 23–26 | MR | Zbl

[10] Pirio L., Équations fonctionnelles abéliennes et géométrie des tissus, Ph. D. Thesis, Univ. Paris-6, 2004, P. 1–267

[11] Poincaré H., “Sur les surfaces de translation et les fonctions abéliennes”, Bull. Soc. Math. France, 29 (1901), 61–86 | MR | Zbl

[12] Chern S. S., Griffiths P. A., “An inequality for the rank of a web and webs of maximum rank”, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4), 5:3 (1978), 539–557 | MR | Zbl

[13] Chern S. S., Griffiths P. A., “Abel's theorem and webs”, Jahresber. Deutsch. Math.-Verein., 80:1–2 (1978), 13–110 | MR | Zbl

[14] Lie S., “Bestimmung aller Flächen, die in mehrfacher Weise durch Translationsbewegung einer Kurve erzeugt werden”, Lie Arch., VII (1882), 155–176 | Zbl

[15] Akivis M. A., Goldberg V. V., Lychagin V. V., “Linearizability of $d$-webs, $d\geq4$, on two-dimensional manifolds”, Selecta Math., 10:4 (2004), 431–451 | DOI | MR | Zbl

[16] Goldberg V. V., “Four-webs in the plane and their linearizability”, Acta Appl. Math., 80:1 (2004), 35–55 | DOI | MR | Zbl

[17] Goldberg V. V., Theory of multicodimensional $(n+1)$-webs, Kluwer Academic Publishers, Dordrecht, 1988, xxii + 466 pp. | MR | Zbl

[18] Abel N. H., “Mémoire sur une propriété générale d'une classe très etendue de fonctions transcendentes”, ØE uvres Complètes de Niels Henrik Abel, new ed., Imprimerie de Grøndahl Son, Christiania; Vol. 1, Ch. 12, 1881; L. Sylow, S. Lie (eds.), Reprint of the second (1881) edition, Éditions Jacques Gabay, Sceaux, 1992, viii+621 pp. ; Mémoires presentes par divers savants, First published, t. VII, 1841 | MR

[19] Griffiths P. A., “On Abel's differential equations”, Algebraic Geometry, J. J. Sylvester Sympos. (Johns Hopkins Univ., Baltimore, Md., 1976), Johns Hopkins Univ. Press, Baltimore, Md, 1977, 26–51 | MR | Zbl

[20] Goldberg V. V., Lychagin V. V., “On the Blaschke conjecture for $3$-webs”, J. Geom. Anal., 16:1 (2006), 69–115 | MR | Zbl

[21] Kruglikov B., Lychagin V. V., “Multi-brackets of differential operators and compatibility of PDE systems”, C. R. Acad. Sci. Paris, Ser. I, 342 (2006), 557–561 | MR | Zbl

[22] Blaschke W., Dubourdieu J., “Invarianten von Kurvengeweben”, Abh. Math. Sem. Univ. Hamburg, 6 (1928), 198–215 | DOI | Zbl

[23] Ripoll O., “Determination du rang des tissus du plan et autres invariants geometriques”, C. R. Math. Acad. Sci. Paris, 341:4 (2005), 247–252 | MR | Zbl

[24] Mayrhofer K., “Kurvensysteme auf Flächen”, Math. Z., 28 (1928), 728–752 | DOI | MR | Zbl

[25] Griffiths P. A., “Variations on a theorem of Abel”, Invent. Math., 35 (1976), 321–390 | DOI | MR | Zbl

[26] Rogers L. J., “On function sum theorems connected with the series $\sum\limits_{n=1}^\infty\frac{x^n}{n^2}$”, London Math. Soc. Proc. (2), 4 (1907), 169–189 | DOI

[27] Lewin L., Polylogarithms and associated functions, North-Holland Publishing Co., New York, 1981, xvii+359 pp. | MR | Zbl

[28] Pirio L., “Sur les tissus plans de rang maximum et le problème de Chern”, C. R. Acad. Sci. Paris, Ser. I, 339:2 (2004), 131–136 | MR | Zbl