, Differential geometry of webs, Handbook of differential geometry, pp.1-152, 2000.
, Ricerche sulle superficie dello spazio a cinque dimensioni e nuove caratterizzazioni della superficie di Veronese, Mathematische Zeitschrift, vol.42, issue.1, pp.411-429, 1937.
DOI : 10.1007/BF01160088
, Determinazione e studio di superficie diS 5 le cui linee principali presentano una notevole particolarit??, Annali di Matematica Pura ed Applicata, Series 4, vol.18, issue.1, pp.51-76, 1939.
DOI : 10.1007/BF02413766
, Tipi notevoli di 5-tessuti di curve piane, Boll. Un. Mat. Ital, vol.1, issue.2, pp.7-11, 1939.
, Elliptic functions, Grundlehren der Mathematischen Wissenschaften, vol.281, 1985.
DOI : 10.1007/978-3-642-52244-4
, Abel's theorem and webs-2, 13-110. Corrections and addenda to our paper : " Abel's theorem and webs, Jahresber. Deutsch. Math.-Verein. Jahresber. Deutsch. Math.-Verein, vol.80, issue.83 2, pp.78-83, 1978.
, The Legacy of Abel in Algebraic Geometry, in The Legacy of Niels Henrik Abel, The Abel Bicentennial, pp.179-205, 2002.
, On planar web geometry through abelian relations and connections, Annals of Mathematics, vol.159, issue.1, pp.425-445, 2004.
DOI : 10.4007/annals.2004.159.425
, Elliptic functions and applications, Applied Mathematical Sciences, vol.80, 1989.
DOI : 10.1007/978-1-4757-3980-0
, Abelian functional equations, planar web geometry and polylogarithms, Selecta Mathematica, vol.11, issue.3-4, 2004.
DOI : 10.1007/s00029-005-0012-y
URL : https://hal.archives-ouvertes.fr/hal-00132906
, que son inverse ?[ ] (notée W) qui jouent des rôles importants pour les calculs : M:=Transpose(VandermondeMatrix(<e
, On construit ses coefficients ? [k,s] p,q (notés Omega[k,s][p,q]) un par un
, on calcule sa courbure en utilisant les procédures introduites plus haut
, x,y),x)+diff(e[i] (x,y)^2,y)): delta[2,0][3,i]:=e[i](x,y)^2*diff(e[i](x,y),x,x)+diff(aa[i],y)+diff(e[i](x,y) ,x)*aa[i]: end do: LL[3]
, On construit ces coefficients ? [k,s] p,q (notés Omega[k,s][p,q]) un par un, avec les lignes de commandes suivantes : for p from 3 to 5 do for q from 3 to 5 do Omega[0,0][p-1,q-1]:=add(e[k](x,y)^(p-1)*(Theta[1,0], y)^(p-1)*(DX+e[k](x,y)*DY)*W[k,r]*L[1,0] [r-1,q-1],r=2..3),k=1..5): end do: end do
, =0: Omega[0,1][4,3]:=-sigma[2]*DY: Omega[0,1][4,4]:=DX+sigma[1]*DY: Omega[0,2][4,4]:=0 : for p from 4 to 5 do for q from 4 to 5 do Omega, k=1..5): end do: end do: for p from 4 to 5 do for q from 3
, =DY: Omega[1,2][4,4]:=DX+sigma[1]*DY: for q from 3 to 5 do Omega
, on calcule sa courbure en utilisant les procédures introduites plus haut : COURBUREPANTAZI:=simplify(matadd(DIFEXTMATRIX(MATRICEPANTAZI),WEDGE MATRIX(MATRICEPANTAZI,MATRICEPANTAZI)))
, définie en 5.1.1.2 ` a l'aide de la procédure suivante : for s from 0 to n-2 do LL[n,s]:=0: end do
, The Legacy of Niels Henrik Abel ? the Abel Bicentennial, 2002.
, Geometry of algebraic curves, Grundlehren der Mathematischen Wissenschaften, 1985.
, Functional equations in several variables, Encyclopedia of Mathematics and its Applications, 1989.
, Geometry and algebra of multidimensional three-webs, Mathematics and its Applications, vol.82, 1992.
, Projective differential geometry of submanifolds, North- Holland Mathematical Library 49, 1993.
, Differential geometry of webs, in " Handbook of differential geometry, pp.1-152, 2000.
, Linearizability of d-webs, d ? 4, on twodimensional manifolds, eprint arXiv:math, p.209290, 2002.
, Exterior differential systems, Mathematical Sciences Research Institute Publications, vol.18, 1991.
, Invarianten von Kurvengeweben, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.6, issue.1, pp.198-215, 1928.
DOI : 10.1007/BF02940610
, ??ber die Tangenten einer ebenen algebraischen Kurve, Uber die Tangenten einer ebenen algebraischen Kurve, pp.166-172, 1932.
DOI : 10.1007/BF02940641
, Topologische fragen der differentialgeometrie 56, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.10, issue.1, pp.180-200, 1934.
DOI : 10.1007/BF02940673
, Higher regulators, algebraic K-theory, and zeta functions of elliptic curves, CRM Monograph Series, vol.11, 2000.
, Ueber Geradengewebe, Annali di Matematica Pura ed Applicata, Series 4, vol.8, issue.1, pp.45-58, 1938.
DOI : 10.1007/BF02410695
, Topologische fragen der differentialgeometrie 57, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.10, issue.1, pp.317-324, 1934.
DOI : 10.1007/BF02940684
, Ricerche sulle superficie dello spazio a cinque dimensioni e nuove caratterizzazioni della superficie di Veronese, Mathematische Zeitschrift, vol.42, issue.1, pp.411-429, 1937.
DOI : 10.1007/BF01160088
, IntroductionàIntroduction`Introductionà la géométrie projective différentielle des surfaces, Gauthier-Villars Théorèmes de type Fuchs pour les tissus feuilletés, Complex analytic methods in dynamical systems, Astérisque, vol.222, pp.49-92, 1931.
, My mathematical education, in Chern?a great geometer of the twentieth century, pp.1-17, 1992.
, Abel's Theorem and Webs, Jahresber. Deutsch. Math.-Verein, vol.80, pp.13-110, 1978.
, An inequality for the rank of a web and webs of maximum rank, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.5, issue.4, pp.539-557, 1978.
, Arithmétique de la fonction zêta, dans La fonction zêta, Ec. Polytech, pp.37-164, 2003.
, Geometry in Grassmannians and a generalization of the dilogarithm, Advances in Mathematics, vol.44, issue.3, pp.279-312, 1982.
DOI : 10.1016/0001-8708(82)90040-8
, Theory of multicodimensional (n + 1)-webs, Mathematics and its Applications, vol.44, 1988.
DOI : 10.1007/978-94-009-3013-1
, The classical polylogarithms, algebraic K-theory and ? F (n), The Gelfand Mathematical Seminars, Birkhäuser, pp.3-135, 1990.
, The intermediate Jacobian of the cubic threefold, Ann. of Math, vol.95, pp.281-356, 1972.
, Principles of algebraic geometry, 1994.
, On the linearizability of 3-webs, Nonlinear Anal, pp.2643-2654, 2001.
, Cartan for beginners: differential geometry via moving frame and exterior differential systems, 2003.
, Ondes oscillantes semi-linéaires en une dimension, Journées " Equations aux dérivées partielles, Ecole polytechnique, 1986.
DOI : 10.5802/jedp.316
URL : http://archive.numdam.org/article/JEDP_1986____A11_0.pdf
, Lines on projective varieties, J. Reine Angew, vol.562, pp.1-3, 2003.
, A Treatise on Projective Differential Geometry, 1942.
, Polylogarithms and Associated Functions, 1981.
, Global web geometry on projective surfaces, en préparation
, RECENT PROGRESS OF GAUSS-SCHWARZ THEORY AND RELATED GEOMETRIC STRUCTURES, Memoirs of the Faculty of Science, Kyusyu University. Series A, Mathematics, vol.47, issue.2, pp.283-381, 1993.
DOI : 10.2206/kyushumfs.47.283
, Algebraic geometry I, Classics in Mathematics, Complex projective varieties , Reprint of the 1976 edition, 1995.
, Abelian functional equations, planar web geometry and polylogarithms, Selecta Math
, Une famille de 5-tissus plans exceptionnels
DOI : 10.1007/s00208-015-1244-6
URL : https://hal.archives-ouvertes.fr/hal-00132907
, On Function Sum Theorems Connected with the Series ???n=1???xnn2, Proceedings of the London Mathematical Society, vol.2, issue.1
DOI : 10.1112/plms/s2-4.1.169
, On certain problems of uniqueness in the theory of webs, Vol?. Mat. Sb. Vyp, vol.2, pp.128-135, 1964.
, Un teoreme topologico sulle schiere di curve e una caratterizzazione geometrica sulle superficie isotermo-asintotiche, Boll. Un. Mat. Ital. Bologna, vol.6, pp.80-85, 1927.