On holomorphic automorphisms of a class of non-homogeneous rigid hypersurfaces in ℂ ^N+1

Abstract

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in ℂ ^N+1 near the origin, and the connected component containing the identity transformation of all locally holomorphic automorphisms of these hypersurfaces near the origin.

Keywords

Real-analytic infinitesimal CR automorphisms / Rigid hypersurfaces / Holomorphic automorphisms

References

[1] Arbatskii A. F.. On the structure of groups of nonlinear automorphisms of (3, 3)-quadrics (in Russian). Mat. Zametki, 1996, 59(2): 163-173 translated in Math. Notes, 59(1–2), 1996, 116–122

[2] Baouendi M. S., Ebenfelt P., Rothschild L. P.. Real submanifolds in complex space and their mappings, 1999, Princeton, NJ: Princeton Univ. Press

[3] Baouendi M. S., Ebenfelt P., Rothschild L. P.. CR automorphisms of real analytic manifolds in complex space. Comm. Anal. Geom., 1998, 6(2): 291-315

[4] Baouendi M. S., Rothschild L. P.. Local holomorphic equivalence of real analytic submanifolds in ℂ^N, 1999, Cambridge: Cambridge Univ. Press 1-24

[5] Beloshapka V. K.. Holomorphic transformations of a quadric (in Russian). Mat. Sb., 1991, 182(2): 203-219

[6] Beloshapka V. K.. Polynomial models of real manifolds (in Russian). Izv. Ross. Akad. Nauk Ser. Mat., 2001, 65(4): 3-20

[7] Beloshapka V. K.. Real submanifolds of a complex space: their polynomial models, automorphisms, and classification problems (in Russian). Uspekhi Mat. Nauk, 2002, 57(1): 3-44

[8] Ebenfelt P., Lamel B., Zaitsev D.. Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case. Geom. Funct. Anal., 2003, 13(3): 546-573

[9] Ežov V., Schmalz G.. Holomorphic automorphisms of quadrics. Math. Z., 1994, 216(3): 453-470

[10] Huang X. J., Ji S. Y., Xu D. K.. Several results for holomorphic mappings from B ⁿ into B ^N, Geometric analysis of PDE and several complex variables, 2005, Providence, RI: A. M. S. 267-292

[11] Huang X. J., Ji S. Y., Xu D. K.. A new gap phenomenon for proper holomorphic mappings from Bn into B ^N. Math. Res. Lett., 2006, 13(4): 515-529

[12] Kolář M.. Local symmetries of finite type hypersurfaces in ℂ². Sci. China Ser. A, 2006, 49(11): 1633-1641

[13] Palinchak N. F.. Quadrics of high codimension (in Russian). Mat. Zametki, 1994, 55(5): 110-115

[14] Palinchak N. F.. Real quadrics of codimension 3 in ℂ⁶ and their nonlinear automorphisms (in Russian). Izv. Ross. Akad. Nauk Ser. Mat., 1995, 59(3): 159-178

[15] Shananina E. N.. Polynomial models of degree 5 and algebras of their automorphisms (in Russian). Mat. Zametki, 2004, 75(5): 757-772

[16] Shevchenko S. N.. Description of the algebra of infinitesimal automrophisms of quadrics of codimension two and their classification (in Russian). Mat. Zametki, 1994, 55(5): 142-153

[17] Stanton N. K.. Infinitesimal CR automorphisms of rigid hypersurfaces. Amer. J. Math., 1995, 117(1): 141-167

[18] Stanton N. K.. Infinitesimal CR automorphisms of real hypersurfaces. Amer. J. Math., 1996, 118(1): 209-233

[19] Wang W.. The Teichmüller distance on the space of spherical CR structures. Sci. China Ser. A, 2006, 49(11): 1523-1538