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On the classification theorem for CR mappings

Published online by Cambridge University Press:  22 January 2016

Atsushi Hayashimoto*
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan, ahayashi@math.nagoya-u.ac.jp
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Abstract.

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Let f: MM′ be a real analytic CR mapping between hyper-surfaces with f(p) = q, where pM and qM′. In this paper, the relation between the type at p and the one at q is considered. As a corollary of the type condition theorem (Theorem 1.1), a classification theorem, which states that under certain type condition, any real analytic CR mapping as above is constant, is proved.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Baouendi, M. S. and Rothschild, L. P., Germs of CR maps between real analytic hypersurfaces, Invent. Math., 93 (1988), 481500.Google Scholar
[2] Lawson, B., Remarks on the generic rank of a CR mappings, J. Geom. Analysis, 2 (1992), 19.Google Scholar
[3] Bloom, T. and Graham, I., On ’type’ conditions for generic real submanifolds of ℂn , Invent.Math., 40 (1977), 217243.Google Scholar
[4] Boggess, A., CR manifolds and the tangential Cauchy-Riemann complex, CRC Press, 1991.Google Scholar
[5] Hayashimoto, A., Application of the Cw -extendability theorem for proper holomorphic mappings to the classification of the mappings between two pseudoellipsoids, Math. Japon, 44 no. 2 (1996), 221237.Google Scholar
[6] Landucci, M., On the proper holomorphic equivalence for a class of pseudoconvex domains, Trans. Amer. Math. Soc, 282 (1988), 807811.Google Scholar