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

Title & Authors
FINITENESS OF INFINITESIMAL DEFORMATIONS OF CR MAPPINGS OF CR MANIFOLDS OF NONDEGENERATE LEVI FORM
Cho, Chung-Ki; Han, Chong-Kyu;

Abstract
Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m ＋ 1 and 2n ＋ 1, respectively, where 1 $\small{\leq}$ m $\small{\leq}$ 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.
Keywords
CR manifold;CR mapping;tangential Cauchy-Riemann equations;infinitesimal deformation;complete system;
Language
English
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References
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.

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

7.
C.-K. Han, Analyticity of CR equivalence between real hypersurfaces in $C^n$ with degenerate Levi form, Invent. Math. 73 (1983), 51-69.

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

9.
C.-K. Han, Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms, Math. Ann. 309 (1997), 401-409

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

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

18.
N. Stanton, Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118 (1996), 209-233

19.
S. M. Webster, The rigidity of CR hypersurfaces in a sphere, Indiana Univ. Math. J. 28 (1979), 405-416.

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.