Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 1949-1958.doi: 10.1007/s10473-021-0611-5

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FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

Wei CHEN, Yingxiang CHEN, Wanke YIN   

  1. 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).

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

CLC Number: 

  • 32T25
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