Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures
Venturi, Irene
Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009), p. 99-127 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2009-01-01
@article{RSMUP_2009__122__99_0,
     author = {Venturi, Irene},
     title = {Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {122},
     year = {2009},
     pages = {99-127},
     mrnumber = {2582833},
     zbl = {1219.17005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2009__122__99_0}
}

Venturi, Irene. Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures. Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009) pp. 99-127. http://gdmltest.u-ga.fr/item/RSMUP_2009__122__99_0/

[1] T. P. Branson - A. Cap - M. Eastwood - A.R. Gover, Prolongations of geometric overdetermined systems, Internat. J. Math. 17, no. 6 (2006), pp. 641-664. | MR 2246885 | Zbl 1101.35060

[2] R. L. Bryant - S.S. Chern - R.B. Gardner - H. Goldschmidt - P.A. Griffiths, Exterior differential systems, M.S.R.I. Publications (Springer, 1991). | MR 1083148 | Zbl 0726.58002

[3] M. Cowling - A.H. Dooley - A. Korányi - F. Ricci, H-type groups and Iwasawa decompositions, Adv. Math., 87 (1991), pp. 1-41. | MR 1102963 | Zbl 0761.22010

[4] M. Cowling - F. De Mari - A. Korányi - H. M. Reimann, Contact and conformal mappings in parabolic geometry. I, Geometriae Dedicata, 111 (2005), pp. 65-86. | MR 2155176 | Zbl 1091.53030

[5] M. Cowling - F. De Mari - A. Korányi - H. M. Reimann, Contact and conformal maps on Iwasawa N groups. Rend. Mat. Acc. Lincei s. 9, 13 (2002), 219-232. | MR 1984102 | Zbl pre02217218

[6] A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generatted by composition of quadratic forms, Trans. Amer. Math. Soc., 258 (1980),pp. 147-153. | MR 554324 | Zbl 0393.35015

[7] H. Goldschmidt, Integrability criteria for systems of nonlinear partial differential equations, J. Differential Geometry, 1 (1967), pp. 269-307. | MR 226156 | Zbl 0159.14101

[8] H. Goldschmidt, Prolongations of linear partial differential equations. I. A conjecture of Elie Cartan, Ann. Sci. École Norm. Sup. (4), 1 (1968), pp. 417-444. | Numdam | MR 235584 | Zbl 0167.09402

[9] H. Goldschmidt, Prolongations of linear partial differential equations. II. Inhomogeneous equations., Ann. Sci. École Norm. Sup. (4), 1 (1968), pp. 617-625. | Numdam | MR 243557 | Zbl 0172.13602

[10] A. Korányi, Multicontact maps: results and conjectures. Lecture notes of Seminario Interdisciplinare di Matematica., IV, pp. 57-63, Lect. Notes Semin. Interdiscip. Mat., IV, S.I.M. Dep. Mat. Univ. Basilicata (Potenza, 2005). | MR 2222536 | Zbl 1109.53028

[11] A. Korányi - H. M. Reimann, Quasiconformal mappings on the Heisenberg group. Invent. Math., 80, n. 2 (1985), pp. 309-338. | MR 788413 | Zbl 0567.30017

[12] F. De Mari - M. A. Shayman, Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix, Acta Appl. Math., 12 (1988), pp. 213-235. | MR 973945 | Zbl 0661.65041

[13] F. De Mari - C. Procesi - M. A. Shayman, Hessenberg varieties, Trans. Amer. Math. Soc., 332 (1992), pp. 529-534. | MR 1043857 | Zbl 0770.14022

[14] M. Eastwood, Real 3-dimensional CR geometry, unpublished manuscript (2004).

[15] T. Morimoto, Geometric structures on filtered manifolds, Hokkaido Math.J., 22, no. 3 (1994), pp. 263-347. | MR 1245130 | Zbl 0801.53019

[16] A. Ottazzi, Multicontact Vector Fields on Hessenberg Manifolds, Journal of Lie Theory, 15 (2005), pp. 357-377. | MR 2147433 | Zbl 1077.22019

[17] P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2), 129, no. 1 (1989), pp. 1-60. | MR 979599 | Zbl 0678.53042

[18] H. M. Reimann, Rigidity of H-type groups, Math. Z., 237 (2001), pp. 697-725. | MR 1854087 | Zbl 0982.22013

[19] N. Tanaka, On differential systems, graded Lie algebras and pseudo-groups, J. Math. Kyoto Univ., 10 (1970), pp. 1-82. | MR 266258 | Zbl 0206.50503

[20] K. Yamaguchi, Differential systems associated with simple graded Lie algebras. In: Progress in differential geometry, Adv. Stud. Pure Math., 22, Math. Soc. Japan (Tokyo, 1993), pp. 413-494. | MR 1274961 | Zbl 0812.17018

[21] T. Yatsui, On pseudo-product graded Lie algebras, Hokkaido Math. J., 17, no. 3 (1988), pp. 333-343. | MR 965191 | Zbl 0658.17018

[22] B. Warhurst, Contact and quasiconformal mappings on real model filiform groups, Bull. Austral. Math. Soc., 68, no. 2 (2003), pp. 329-343. | MR 2016308 | Zbl 1061.53025

[23] B. Warhurst, Jet spaces as nonrigid Carnot groups, J. Lie Theory, 15, no. 1 (2005), pp. 341-356. | MR 2115247 | Zbl 1079.53062

[24] B. Warhurst, Tanaka prolongation of free Lie algebras, Geom. Dedicata, 130 (2007), pp. 59-69. | MR 2365778 | Zbl pre05248752