Contact geometry and CR-structures on spheres

John Bland; Tom Duchamp

Banach Center Publications (1995)

  • Volume: 31, Issue: 1, page 99-113
  • ISSN: 0137-6934

Abstract

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A normal form for small CR-deformations of the standard CR-structure on the (2n+1)-sphere is presented. The space of normal forms is parameterized by a single function on the sphere. For n>1, the normal form is used to obtain explicit embeddings into ℂ n + 1 . For n=1, the cohomological obstruction to embeddability is identified.

How to cite

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Bland, John, and Duchamp, Tom. "Contact geometry and CR-structures on spheres." Banach Center Publications 31.1 (1995): 99-113. <http://eudml.org/doc/262751>.

@article{Bland1995,
abstract = {A normal form for small CR-deformations of the standard CR-structure on the (2n+1)-sphere is presented. The space of normal forms is parameterized by a single function on the sphere. For n>1, the normal form is used to obtain explicit embeddings into $ℂ^\{n+1\}$. For n=1, the cohomological obstruction to embeddability is identified.},
author = {Bland, John, Duchamp, Tom},
journal = {Banach Center Publications},
keywords = {deformation theory; convex domains; moduli; Riemann maps; contact geometry; CR-structures},
language = {eng},
number = {1},
pages = {99-113},
title = {Contact geometry and CR-structures on spheres},
url = {http://eudml.org/doc/262751},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Bland, John
AU - Duchamp, Tom
TI - Contact geometry and CR-structures on spheres
JO - Banach Center Publications
PY - 1995
VL - 31
IS - 1
SP - 99
EP - 113
AB - A normal form for small CR-deformations of the standard CR-structure on the (2n+1)-sphere is presented. The space of normal forms is parameterized by a single function on the sphere. For n>1, the normal form is used to obtain explicit embeddings into $ℂ^{n+1}$. For n=1, the cohomological obstruction to embeddability is identified.
LA - eng
KW - deformation theory; convex domains; moduli; Riemann maps; contact geometry; CR-structures
UR - http://eudml.org/doc/262751
ER -

References

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  1. [B] J. Bland, Contact geometry and CR-structures on S 3 , Acta Math. 172 (1994), 1-49. Zbl0814.32002
  2. [BD1] J. Bland and T. Duchamp, Moduli for pointed convex domains, Invent. Math. 104 (1991), 61-112. Zbl0731.32010
  3. [BD2] J. Bland and T. Duchamp, Basepoint dependence of moduli for convex domains, in preparation (1993). 
  4. [BdM] L. Boutet de Monvel, Intégration des équations de Cauchy-Riemann induites formelles, Séminaire Goulaouic-Lions-Schwartz 9 (1974/75), 1-13. 
  5. [BE] D. M. Burns and C. L. Epstein, Embeddability for three dimensional CR-manifolds, J. Amer. Math. Soc. 3 (1990), 809-841. Zbl0736.32017
  6. [CL] J. H. Cheng and J. Lee, A local slice theorem for 3-dimensional CR-structures, preprint. Zbl0841.32004
  7. [FS] G. B. Folland and E. M. Stein, Estimates for the ∂ ̅ b -complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. Zbl0293.35012
  8. [G] J. Gray, Some global properties of contact structures, Ann. of Math. 69 (1959), 421-450. Zbl0092.39301
  9. [L1] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. 
  10. [L2] L. Lempert, On three dimensional Cauchy-Riemann manifolds, J. Amer. Math. Soc. 5 (1992), 923-969. Zbl0781.32014
  11. [O] H. Omori, Infinite Dimensional Lie Transformation Groups, Lecture Notes in Math. 427, Springer, Berlin, 1994. Zbl0328.58005
  12. [R] H. Rossi, Attaching analytic spaces to an analytic space along a pseudoconvex boundary, in: Proceedings of the Conference on Complex Manifolds, A. Aeppli et al. (ed.), Springer, Berlin, 1965, 242-256. 
  13. [W] A. Weinstein, Lectures on Symplectic Manifolds, CBMS Regional Conf. Ser. in Math. 29, Amer. Math. Soc., Providence, 1977. 

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