Advertisement

Russian Journal of Mathematical Physics

, Volume 26, Issue 1, pp 1–8 | Cite as

Polynomial Model CR-Manifolds with the Rigidity Condition

  • V. K. BeloshapkaEmail author
Article
  • 10 Downloads

Abstract

In the present paper, the results recently obtained by the author for model manifolds with the Hörmander numbers (2,3) without the condition of complete nondegeneracy are extended to an arbitrary Bloom–Graham type. Here a simplifying assumption is made that the model surface is rigid.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. K. Beloshapka, “Universal Models for Real Submanifolds,” Mat. Zametki 75 (4), 507–522 (2004) [Math. Notes 75 (4), 475–488 (2004)].MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Th. Bloom and I. Graham, “On Type Conditions for Generic Real Submanifolds of C n,” Invent. Math. 40, 217–243 (1977).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    V. K. Beloshapka, “A Cubic Model of a Real Manifold,” Mat. Zametki 70 (4), 503–519 (2001) [Math. Notes 70 (4), 457–470 (2001)].MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    R. V. Gammel and I. G. Kossovskii, “The Envelope of Holomorphy of a Model Third–Degree Surface and the Rigidity Phenomenon,” Tr. Mat. Inst. Steklova 253, 30–45 (2006) [Proc. Steklov Inst. Math. 253, 22–36 (2006)].zbMATHGoogle Scholar
  5. 5.
    M. Sabzevari, “Biholomorphic Equivalence to Totally Nondegenerate Model CR Manifolds,” Ann. Mat. Pura Appl., (2018), doi: 10.1007/s10231–018–0812–2.Google Scholar
  6. 6.
    M. Sabzevari and A. Spiro, “On the Geometric Order of Totally Nondegenerate CR–manifolds,” arXiv: 1807.03076v1 [mathCV], 9 Jul 2018.Google Scholar
  7. 7.
    J. Gregorovich, “On the Beloshapka’s Rigidity Conjecture for Real Submanifolds in Complex Space,” arXiv: 1807.03502v1 [mathCV], 10 Jul 2018.Google Scholar
  8. 8.
    V. K. Beloshapka, “Cubic Model CR–manifolds without the Assumption of Complete Nondegeneracy,” Russ. J. Math. Phys. 25 (2), 148–157 (2018).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    V. K. Beloshapka, “Moduli Space of Model Real Submanifolds,” Russ. J. Math. Phys. 13 (3), 245–252 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    N. Stanton, “Infinitesimal CR–Automorphisms,” Amer. J. Math. 118, 209–233 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. S. Baouendi, P. Ebenfelt, and L. P. Rothschild, “CR Automorphisms of Real Analytic CR in Complex Space,” Comm. Anal. Geom. 6, 291–315 (1998).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    H. Poincaré, “Les fonctions analytiques de deux variables et la représentation conforme,” Rend. Circ. Mat. Palermo 23, 185–220 (1907).CrossRefzbMATHGoogle Scholar
  13. 13.
    N. Tanaka, “On the Pseudo–Conformal Geometry of Hypersurfaces of the Space of N Complex Variables,” J. Math. Soc. Japan 14, 397–429 (1962).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    W. Kaup, “Einige Bemerkungen uber polynomiale Vektorfelder, Jordanalgebren und die Automorphismen von Siegelschen Gebieten,” Math. Ann. 204, 131–144 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    A. E. Tumanov, “Finite–Dimensionality of the Group of CR Automorphisms of a Standard CR Manifold, and Proper Holomorphic Mappings of Siegel Domains,” Izv. Akad. Nauk SSSR Ser. Mat. 52 (3), 651–659 (1988) [Math. USSR Izv. 32 (3), 655–662 (1989)].zbMATHGoogle Scholar
  16. 16.
    A. Huckleberry and D. Zaitsev, “Actions of Groups of Birationally Extendible Automorphisms,” Geometric complex analysis (Hayama, 1995), 261–285, World Sci. Publ., River Edge, NJ, (1996).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations