On the real-analytic infinitesimal CR automorphism of hypersurfaces of infinite type
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Abstract
We consider a real smooth hypersurface M ⊂ C2, which is of D’Angelo infinite type at p 2 M. The purpose of this paper is to show that the real vector space of tangential holomorphic vector field germs at p vanishing at p is either trivial or of real dimension 1.
Article Details
Keywords
Holomorphic vector field, infinitesimal CR automorphism, real hypersurface, infinite type point.
References
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[2] Byun, J., Joo J.-C. and Song M., The characterization of holomorphic vector fields vanishing at an infinite type point, J. Math. Anal. Appl. 387 (2012), 667{675.
[3] Chern, S. S. and Moser, J. K., Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219{271.
[4] Coleman, C., Equivalence of planar dynamical and differential systems, J. Differential Equations 1 (1965), 222{233.
[5] D’Angelo, J. P. , Real hypersurfaces, orders of contact, and applications, Ann. Math. 115 (1982), 615{637.
[6] Garijo, A. , Gasull, A. and Jarque, X., Local and global phase portrait of equation z_ = f(z), Discrete Contin. Dyn. Syst. 17 (2) (2007), 309{329.
[7] Kol´aˇr, M. and Meylan, F., Infinitesimal CR automorphisms of hypersurfaces of finite type in C2, Arch. Math. (Brno) 47 (5) (2011), 367{375.
[8] Kim, K.-T. and Ninh, V. T., On the tangential holomorphic vector fields vanishing at an infinite type point, Trans. Amer. Math. Soc. 367 (2015), no. 2, 867{885.
[9] Ninh, V. T., On the existence of tangential holomorphic vector fields vanishing at an infinite type point, arXiv:1303.6156v5.
[10] Stanton, N., Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118 (1) (1996), 209{233.
[11] Stanton, N., Infinitesimal CR automorphisms of rigid hypersurfaces, Amer. J. Math. 117 (1) (1995), 141{167.
[12] Sverdlove, R., Vector fields defined by complex functions, J. Differential Equations 34 (1979), no. 3, 427{439.