FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

doi:10.1007/s10473-021-0611-5

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 1949-1958.doi: 10.1007/s10473-021-0611-5

FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

陈伟, 陈颖祥, 尹万科

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2021-03-30 修回日期:2021-09-10 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Wanke YIN,E-mail:wankeyin@whu.edu.cn E-mail:wankeyin@whu.edu.cn
作者简介:Wei CHEN,E-mail:cwwh102013@whu.edu.cn;Yingxiang CHEN,E-mail:yingxiangchen09@whu.edu.cn
基金资助:
The third author was supported in part by NSFC (12171372).

FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

Wei CHEN, Yingxiang CHEN, Wanke YIN

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2021-03-30 Revised:2021-09-10 Online:2021-12-25 Published:2021-12-27
Supported by:
The third author was supported in part by NSFC (12171372).

摘要/Abstract

摘要： Let $M$ be a smooth pseudoconvex hypersurface in $\mathbb{C}^{n+1}$ whose Levi form has at most one degenerate eigenvalue. For any tangent vector field $L$ of type $(1,0)$, we prove the equality of the commutator type and the Levi form type associated to $L$. We also show that the regular contact type, the commutator type and the Levi form type of the real hypersurface are the same.

关键词: pseudoconvex hypersuface, finite type, Levi form, holomorphic vector field

Abstract: Let $M$ be a smooth pseudoconvex hypersurface in $\mathbb{C}^{n+1}$ whose Levi form has at most one degenerate eigenvalue. For any tangent vector field $L$ of type $(1,0)$, we prove the equality of the commutator type and the Levi form type associated to $L$. We also show that the regular contact type, the commutator type and the Levi form type of the real hypersurface are the same.

Key words: pseudoconvex hypersuface, finite type, Levi form, holomorphic vector field

中图分类号:

32T25

陈伟, 陈颖祥, 尹万科. FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE[J]. 数学物理学报(英文版), 2021, 41(6): 1949-1958.

Wei CHEN, Yingxiang CHEN, Wanke YIN. FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE[J]. Acta mathematica scientia,Series B, 2021, 41(6): 1949-1958.

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FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

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