Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures

Irene Venturi

Rendiconti del Seminario Matematico della Università di Padova (2009)

  • Volume: 122, page 99-127
  • ISSN: 0041-8994

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Venturi, Irene. "Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures." Rendiconti del Seminario Matematico della Università di Padova 122 (2009): 99-127. <http://eudml.org/doc/108779>.

@article{Venturi2009,
author = {Venturi, Irene},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {nilpotent Lie groups; multicontact structures; rigidity results; Hessenberg algebras},
language = {eng},
pages = {99-127},
publisher = {Seminario Matematico of the University of Padua},
title = {Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures},
url = {http://eudml.org/doc/108779},
volume = {122},
year = {2009},
}

TY - JOUR
AU - Venturi, Irene
TI - Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2009
PB - Seminario Matematico of the University of Padua
VL - 122
SP - 99
EP - 127
LA - eng
KW - nilpotent Lie groups; multicontact structures; rigidity results; Hessenberg algebras
UR - http://eudml.org/doc/108779
ER -

References

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  1. [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. Zbl1101.35060MR2246885
  2. [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). Zbl0726.58002MR1083148
  3. [3] M. COWLING - A.H. DOOLEY - A. KORÁNYI - F. RICCI, H-type groups and Iwasawa decompositions, Adv. Math., 87 (1991), pp. 1-41. Zbl0761.22010MR1102963
  4. [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. Zbl1091.53030MR2155176
  5. [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. Zbl1225.22012MR1984102
  6. [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. Zbl0393.35015MR554324
  7. [7] H. GOLDSCHMIDT, Integrability criteria for systems of nonlinear partial differential equations, J. Differential Geometry, 1 (1967), pp. 269-307. Zbl0159.14101MR226156
  8. [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. Zbl0167.09402MR235584
  9. [9] H. GOLDSCHMIDT, Prolongations of linear partial differential equations. II. Inhomogeneous equations., Ann. Sci. École Norm. Sup. (4), 1 (1968), pp. 617-625. Zbl0172.13602MR243557
  10. [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). Zbl1109.53028MR2222536
  11. [11] A. KORÁNYI - H. M. REIMANN, Quasiconformal mappings on the Heisenberg group. Invent. Math., 80, n. 2 (1985), pp. 309-338. Zbl0567.30017MR788413
  12. [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. Zbl0661.65041MR973945
  13. [13] F. DE MARI - C. PROCESI - M. A. SHAYMAN, Hessenberg varieties, Trans. Amer. Math. Soc., 332 (1992), pp. 529-534. Zbl0770.14022MR1043857
  14. [14] M. EASTWOOD, Real 3-dimensional CR geometry, unpublished manuscript (2004). 
  15. [15] T. MORIMOTO, Geometric structures on filtered manifolds, Hokkaido Math.J., 22, no. 3 (1994), pp. 263-347. Zbl0801.53019MR1245130
  16. [16] A. OTTAZZI, Multicontact Vector Fields on Hessenberg Manifolds, Journal of Lie Theory, 15 (2005), pp. 357-377. Zbl1077.22019MR2147433
  17. [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. Zbl0678.53042MR979599
  18. [18] H. M. REIMANN, Rigidity of H-type groups, Math. Z., 237 (2001), pp. 697-725. Zbl0982.22013MR1854087
  19. [19] N. TANAKA, On differential systems, graded Lie algebras and pseudo-groups, J. Math. Kyoto Univ., 10 (1970), pp. 1-82. Zbl0206.50503MR266258
  20. [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. Zbl0812.17018MR1274961
  21. [21] T. YATSUI, On pseudo-product graded Lie algebras, Hokkaido Math. J., 17, no. 3 (1988), pp. 333-343. Zbl0658.17018MR965191
  22. [22] B. WARHURST, Contact and quasiconformal mappings on real model filiform groups, Bull. Austral. Math. Soc., 68, no. 2 (2003), pp. 329-343. Zbl1061.53025MR2016308
  23. [23] B. WARHURST, Jet spaces as nonrigid Carnot groups, J. Lie Theory, 15, no. 1 (2005), pp. 341-356. Zbl1079.53062MR2115247
  24. [24] B. WARHURST, Tanaka prolongation of free Lie algebras, Geom. Dedicata, 130 (2007), pp. 59-69. Zbl1283.17013MR2365778

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