The local equivalence problem in CR geometry
Archivum Mathematicum (2006)
- Volume: 042, Issue: 5, page 253-266
- ISSN: 0044-8753
Access Full Article
topAbstract
topHow to cite
topReferences
top- Baouendi M. S., Ebenfelt P., Rothschild L. P., Convergence and finite determination of formal CR mappings, J. Amer. Math. Soc. 13 (2000), 697–723. Zbl0958.32033MR1775734
- Baouendi M. S., Ebenfelt P., Rothschild L. P., Local geometric properties of real submanifolds in complex space, Bull. Amer. Math. Soc. (N.S.) 37 (3) (2000), 309–336. MR1754643
- Barletta E., Bedford E., Existence of proper mappings from domains in , Indiana Univ. Math. J. 2 (1990), 315–338. (1990) MR1089041
- Beals M., Fefferman C., Grossman R., Strictly pseudoconvex domains in , Bull. Amer. Math. Soc. 8 (1983), 125–322. (1983) MR0684898
- Beloshapka V. K., On the dimension of the group of automorphisms of an analytic hypersurface, Math. USSR, Izv. 14 (1980), 223–245. (1980) Zbl0456.32015MR0534592
- Beloshapka V. K., Ezhov V. V., Normal forms and model hypersurfaces in , preprint.
- Cartan E., Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes, I, Ann. Math. Pura Appl. 11 (1932), 17–90. (1932)
- Cartan E., Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes, II, Ann. Scuola Norm. Sup. Pisa 1 (1932), 333–354. (1932) MR1556687
- Chern S. S., Moser J., Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. (1974) MR0425155
- D’Angelo J. P., Orders od contact, real hypersurfaces and applications, Ann. of Math. (2) 115 (1982), 615–637. (1982) MR0657241
- Ebenfelt P., New invariant tensors in CR structures and a normal form for real hypersurfaces at a generic Levi degeneracy, J. Differential Geom. 50 (1998), 207–247. (1998) Zbl0945.32020MR1684982
- Ebenfelt P., Lamel B., Zaitsev D., Degenerate real hypersurfaces in with few automorphisms, arXiv:math.CV/0605540.
- Ebenfelt P., Huang X., Zaitsev D., The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics, Amer. J. Math. 127 (2005), 169–191. (191.) MR2115664
- Fefferman C., Parabolic invariant theory in complex analysis, Adv. Math. 31 (1979), 131–262. (1979) Zbl0444.32013MR0526424
- Isaev A. V., Krantz S. G., Domains with non-compact automorphism group: a survey, Adv. Math. 146 (1) (1999), 1–38. (1999) Zbl1040.32019MR1706680
- Jacobowitz H., An introduction to CR structures, Math. Surveys Monogr. 32, AMS 1990. (1990) Zbl0712.32001MR1067341
- Juhlin R., [unknown], PhD-thesis, UCSD Zbl1219.32020
- Kohn J. J., Boundary behaviour of on weakly pseudoconvex manifolds of dimension two, J. Differential Geom. 6 (1972), 523–542. (1972) MR0322365
- Kolář M., Normal forms for hypersurfaces of finite type in , Math. Res. Lett. 12 (2005), 523–542. MR2189248
- Kolář M., Local symmetries of finite type hypersurfaces in , Sci. China A 48 (2006), 1633–1641. MR2288220
- Kowalski R., A hypersurface in whose stability group is not determined by 2-jets, Proc. Amer. Math. Soc. 130 (12) (2002), 3679–3686. (electronic) MR1920048
- Kruzhilin N. G., Loboda A. V., Linearization of local automorphisms of pseudoconvex surfaces, Dokl. Akad. Nauk SSSR 271 (1983), 280–282. (1983) Zbl0582.32040MR0718188
- Poincaré H., Les fonctions analytique de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo 23 (1907), 185–220. (1907)
- Segre B., Intorno al problem di Poincaré della rappresentazione pseudo-conform, Rend. Accad. Lincei 13 (1931), 676–683. (1931)
- Stanton N., A normal form for rigid hypersurfaces in , Amer. J. Math. 113 (1991), 877–910. (1991) MR1129296
- Vitushkin A. G., Real analytic hypersurfaces in complex manifolds, Russ. Math. Surv. 40 (1985), 1–35. (1985) Zbl0588.32025MR0786085
- Webster S. M., On the Moser normal form at a non-umbilic point, Math. Ann. 233 (1978), 97–102. (1978) Zbl0358.32013MR0486511
- Wells R. O., Jr., The Cauchy-Riemann equations and differential geometry, Bull. Amer. Math. Soc. (N.S.) 6 (2) (1982), 187–199. (1982) Zbl0496.32012MR0640945
- Wong P., A construction of normal forms for weakly pseudoconvex CR manifolds in , Invent. Math. 69 (1982), 311–329. (1982) MR0674409
- Zaitsev D., Unique determination of local CR-maps by their jets: A survey, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Suppl. 13 (2002), 295–305. Zbl1098.32018MR1984108