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On the tangential holomorphic vector fields vanishing at an infinite type point


Authors: Kang-Tae Kim and Ninh Van Thu
Journal: Trans. Amer. Math. Soc. 367 (2015), 867-885
MSC (2010): Primary 32M05; Secondary 32H02, 32H50, 32T25
Published electronically: September 4, 2014
MathSciNet review: 3280030
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Abstract: Let $ (M,p)$ be a $ \mathcal C^\infty $ smooth non-Leviflat CR hypersurface germ in $ \mathbb{C}^2$ where $ p$ is of infinite type. The purpose of this article is to investigate the holomorphic vector fields tangent to $ (M,p)$ vanishing at $ p$.


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Additional Information

Kang-Tae Kim
Affiliation: Department of Mathematics and Center for Geometry and its Applications, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
Email: kimkt@postech.ac.kr

Ninh Van Thu
Affiliation: Department of Mathematics and Center for Geometry and its Applications, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea – and – Department of Mathematics, Vietnam National University at Hanoi, 334 Nguyen Trai str., Hanoi, Vietnam
Email: thunv@postech.ac.kr, thunv@vnu.edu.vn

DOI: https://doi.org/10.1090/S0002-9947-2014-05917-5
Keywords: Holomorphic vector field, real hypersurface, infinite type point.
Received by editor(s): June 19, 2012
Published electronically: September 4, 2014
Additional Notes: The research of the authors was supported in part by an NRF grant 2011-0030044 (SRC-GAIA) of the Ministry of Education, The Republic of Korea.
Article copyright: © Copyright 2014 American Mathematical Society