Geodesic
CR Mappings of Circular CR Manifolds
Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 396-407

Voir la notice de l'article provenant de la source Cambridge University Press

Let M be a circular CR manifold and let N be a rigid CR manifold in some complex vector spaces. The problem of the existence of local CR mappings from M into N is considered. Conditions are given which ensure that the space of such CR mappings depends on a finite number of parameters. The idea of the proof of the main result relies on a Bishop type equation for CR mappings. Roughly speaking, we look for CR mappings from M into N in the form F = (ƒ,g), we assume that g is given, then we find ƒ in terms of g and some parameters, and finally we look for conditions on g. It works independently of assumptions on the Levi forms of M and N, and there is also some freedom on the codimension of the manifolds.
DOI : 10.4153/CMB-1995-058-8
Mots-clés : 32C16, 32H99, 58C10, CR mappings, CR manifolds 
Boivin, André. CR Mappings of Circular CR Manifolds. Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 396-407. doi: 10.4153/CMB-1995-058-8
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Baouendi, M. S. and Rothschild, L. P., A generalized complex Hopf Lemma and its applications to CR mappings, Invent. Math. 111(1993), 331–348. Google Scholar

Baouendi, M. S. and Treves, F., A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. Math. 113(1981), 331–348. Google Scholar

Bishop, E., Differentiable manifolds in complex Euclidean space, Duke Math. J. 32((1965)), 1—22. Google Scholar

Boggess, A., CR Manifolds and Tangential Cauchy-Riemann Equations, CRC Press, Stud. Adv. Math. (1991). Google Scholar

Boggess, A. and Pitts, J., CR-extension near a point of higher type, Duke Math. J. 52(1985), 65—102. Google Scholar

Ezhov, V. V. and Schmalz, G., Poincaré automorphisms for nondegenerate quadrics, Math. Ann. 298 (1994), 79–87. Google Scholar

Forstneric, F., Mappings of quadric Cauchy-Riemann manifolds, Math. Ann. 192(1992), 163–180. Google Scholar

Forstneric, F., Proper holomorphic mappings, Proc. of the Special Year held at the Mittag-Leffler Institute, Stockholm, 1987/1988, (ed. J. E. Fornaess), Princeton Univ. Press, Math. Notes 38(1993), 297–363. Google Scholar

Hill, C. D. andTaiani, G., Families of analytic discs in ℂn with boundaries on a prescribed CR submanifold, Ann. Scuola Norm. Sup. Pisa 5(1978), 327–380. Google Scholar

Poincaré, H., Les fonctions analytiques de deux variables et la représentation conforme, Rend. Cire. Mat. Palermo 23(1907), 185–220. Google Scholar

Shimizu, S., Automorphisms of bounded Reinhardt domains, Japan J. Math. 15(1989), 385–414. Google Scholar

J N. Stanton, Infinitesimal CR automorphisms of rigid hypersurfaces in ℂ2, J. Geom. Anal. 1(1991), 231— 267. Google Scholar

J N. Stanton, Infinitesimal CR automorphisms of rigid hypersurfaces, Amer. J. Math. 117(1995), 141—167. Google Scholar

[Su] Sukhov, A., On CR mappings of real quadric manifolds, Michigan Math. J. 41(1994), 143—150. Google Scholar

Tumanov, A. E., Finite-dimensionality of the group of CR automorphisms of a standard CR manifold, and proper holomorphic mappings of Siegel domains, Izv. Akad. Nauk. SSSR Ser. Mat., English transi., Math. USSR-Izv. 32(1988), 655–661. Google Scholar

Vitushkin, A. G., Holomorphic mappings and the geometry of hypersurfaces, Several Complex Variables I, Encyclopaedia Math. Sci., 7, Springer Verlag, 1990, 159–214. Google Scholar

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