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Analytic Jet Parametrization for CR Automorphisms of Some Essentially Finite CR Manifolds

Published online by Cambridge University Press:  11 January 2016

Sung-Yeon Kim
Sung-Yeon Kim*
Affiliation:
Department of Mathematics Education, Kangwon National University, 123 Hyoja-dong, Chuncheon, Kangwon-do, 200-701, Korea, sykim87@kangwon.ac.kr
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Abstract

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In this paper we construct analytic jet parametrizations for the germs of real analytic CR automorphisms of some essentially finite CR manifolds on their finite jet at a point. As an application we show that the stability groups of such CR manifolds have Lie group structure under composition with the topology induced by uniform convergence on compacta.

Keywords

32V4032V20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 189 , 2008 , pp. 155 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

[1] Baouendi, M. S., Ebenfelt, P. and Rothschild, L. P., Algebraicity of holomorphic mappings between real algebraic sets in C”, Acta Math., 177 (1996), 225–273.Google Scholar
[2] Baouendi, M. S., Ebenfelt, P. and Rothschild, L. P., Parametrization of local biholo-morphisms of real analytic hypersurfaces, Asian J. Math., 1 (1997), 1–16.CrossRefGoogle Scholar
[3] Baouendi, M. S., Ebenfelt, P. and Rothschild, L. P., CR automorphisms of real analytic manifolds in complex space, Comm. Anal. geom., 6 (1998), 291–315.Google Scholar
[4] Baouendi, M. S., Ebenfelt, P. and Rothschild, L. P., Real submanifolds in complex space and their mappings, Princeton University Press, Princeton, New Jersey, 1999.Google Scholar
[5] Baouendi, M. S., Ebenfelt, P. and Rothschild, L. P., Rational dependence of smooth and analytic CR mappings on their jets, Math. Ann., 315 (1999), 205–249.Google Scholar
[6] Baouendi, M. S., Ebenfelt, P. and Rothschild, L. P., Convergence and finite determination of formal CR mappings, J. Amer. Math. Soc., 13 (2000), 697–723.Google Scholar
[7] Baouendi, M. S., Rothschild, L. P., Winkelmann, J. and Zaitsev, D., Lie group structures on groups of diffeomorphisms and applications to CR manifolds, Ann. de L’Institut Fourier, 54 (2004), 1279–1303.Google Scholar
[8] Bloom, T. and Graham, I., On type conditions for generic real submanifolds of C”, Invent. Math., 40 (1977), 217–243.Google Scholar
[9] Chern, S. S. and Moser, J. K., Real hypersurfaces in complex manifolds, Acta Math., 133 (1974), 219–271.CrossRefGoogle Scholar
[10] Ebenfelt, P., Finite jet determination of holomorphic mappings at the boundary, Asian J. Math., 5 (2001), 637–662.CrossRefGoogle Scholar
[11] Gunning, R. C., Introduction to holomorphic functions of several variables, Vol. 2, Wordsworth and Brooks/Cole, Belmont, California, 1990.Google Scholar
[12] Han, C. K., Analyticity of CR equivalences between some real hypersurfaces in C” with degenerate Levi forms, Invent. Math., 73 (1983), 51–69.CrossRefGoogle Scholar
[13] Han, C. K., Complete differential system for the mappings of CR manifolds of non-degenerate Levi forms, Math. Ann., 309 (1997), 401–409.Google Scholar
[14] Hayashimoto, A., On the complete system of finite order for CR mappings and its application, Osaka J. of Math., 35 (1998), 617–628.Google Scholar
[15] Kim, S.-Y., Complete system of finite order for CR mappings between real analytic hypersurfaces of degenerate Levi form, J. Korean math. Soc., 38 (2001), 87–99.Google Scholar
[16] Kim, S.-Y. and Zaitsev, D., The equivalence and embedding problems for CR structures of any codimension, Topology, 44 (2005), 557–584.Google Scholar
[17] Kohn, J. J., Boundary behavior of ∂ on weakly pseudo-convex manifolds of dimension two, J. Differential Geom., 6 (1972), 523–542.Google Scholar
[18] Lamel, B., Holomorphic maps of real submanifolds in complex spaces of different dimensions, Pacific J. Math., 201 (2001), 357–387.CrossRefGoogle Scholar
[19] Lamel, B. and Mir, N., Parametrization of local CR automorphisms by finite jets and applications, J. Amer. Math. Soc., to appear.Google Scholar
[20] Webster, S., On the reflection principle in several complex variables, Proc. Amer. Math. Soc., 71 (1978), 26–28.Google Scholar
[21] Zaitsev, D., Germs of local automorphism of real analytic CR structures and analytic dependence on k-jets, Math. Research Letters, 4 (1997), 823–842.Google Scholar