DOI QR코드

DOI QR Code

FINITENESS OF INFINITESIMAL DEFORMATIONS OF CR MAPPINGS OF CR MANIFOLDS OF NONDEGENERATE LEVI FORM

  • 발행 : 2002.01.01

초록

Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m + 1 and 2n + 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.

키워드

참고문헌

  1. M. S. Baouendi, P. Ebenfelt, and L. P. Rothschild, Infinitesimal CR automorphisms of real analytic manifolds in complex space, Comm. Anal. Geom. 6 (1998), 291-315. https://doi.org/10.4310/CAG.1998.v6.n2.a3
  2. M. S. Baouendi, P. Ebenfelt, and L. P. Rothschild, Real submanifolds in complex space and their mappings, Princeton University Press, Priceton N. J., 1999
  3. A. Bogges, CR manifolds and the tangential Cauchy-Riemann complex, CRC Press, Boca Raton, 1991
  4. R. Bryant, S.-S. Chern, R. Gardner, H. Goldschmidt, and P. Griffiths, Exterior differential systems, Springer-Verlag, Berlin, 1991.
  5. D. Burns and S. Shnider, Real hypersurfaces in complex manifolds, Proc. Symp. Pure Math. 30 (1976), 141-167
  6. S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271 https://doi.org/10.1007/BF02392146
  7. C.-K. Han, Analyticity of CR equivalence between real hypersurfaces in $C^n$ with degenerate Levi form, Invent. Math. 73 (1983), 51-69. https://doi.org/10.1007/BF01393825
  8. C.-K. Han, Regularity of isometric immersions of positively curved Riemannian manifolds and its analogy with CR geometry, J. Differential Geom. 28 (1988), 477-484 https://doi.org/10.4310/jdg/1214442474
  9. C.-K. Han, Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms, Math. Ann. 309 (1997), 401-409 https://doi.org/10.1007/s002080050119
  10. A. Hayashimoto, On the complete system of finite order for CR mappings and its application, Osaka J. Math. 35 (1998), 617-628
  11. A. Hayashimoto, On the relation between the holomorphic extendability theorems and the finiteness properties, Contemp. Math. 222 (1999), 219-226 https://doi.org/10.1090/conm/222/03165
  12. C.-K. Han and J.-N. Yoo, A method of prolongation of tangential Cauchy-Riemann equations, Adv. Stud. Pure Math. 25 (1997), 158-166
  13. H. Jacobowitz, Deformation leaving a hypersurface fixed, Proc. Symp. Pure Math. 23 (1971), 343-351
  14. H. Jacobowitz, Introduction to CR structures, Amer. Math. Soc., Providence, 1990
  15. S. Y. Kim, Finiteness and analyticity of pseudo-conformal embeddings, Nagoya Math. J. (to appear)
  16. P. J. Olver, Applications of Lie groups to differential equations, Springer-Verlag, New York, 1993
  17. N. Stanton, Infinitesimal CR automorphisms of rigid hypersurfaces, Amer. J. Math. 117 (1995), 141-167 https://doi.org/10.2307/2375039
  18. N. Stanton, Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118 (1996), 209-233 https://doi.org/10.1353/ajm.1996.0005
  19. S. M. Webster, The rigidity of CR hypersurfaces in a sphere, Indiana Univ. Math. J. 28 (1979), 405-416. https://doi.org/10.1512/iumj.1979.28.28027
  20. D. Zaitsev, Germs of local automorphism of real-analytic CR structures and analytic dependence on k-jets, Math. Research Letters 4 (1997), 823-842. https://doi.org/10.4310/MRL.1997.v4.n6.a4

피인용 문헌

  1. Recent clinical overview of renal and perirenal abscesses in 56 consecutive cases vol.23, pp.3, 2008, https://doi.org/10.3904/kjim.2008.23.3.140
  2. SOLVABILITY OF OVERDETERMINED PDE SYSTEMS THAT ADMIT A COMPLETE PROLONGATION AND SOME LOCAL PROBLEMS IN CR GEOMETRY vol.40, pp.4, 2003, https://doi.org/10.4134/JKMS.2003.40.4.695
  3. On Fuzzy Almost r-minimal Continuous Functions between Fuzzy Minimal Spaces and Fuzzy Topological Spaces vol.11, pp.1, 2011, https://doi.org/10.5391/IJFIS.2011.11.1.044