Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NULLITY OF THE LEVI-FORM AND THE ASSOCIATED SUBVARIETIES FOR PSEUDO-CONVEX CR STRUCTURES OF HYPERSURFACE TYPE

  • Received : 2018.02.23
  • Accepted : 2018.05.29
  • Published : 2019.01.31
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Abstract

Let $M^{2n+1}$, $n{\geq}1$, be a smooth manifold with a pseudoconvex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $M={\mathcal{S}}_0{\supset}{\mathcal{S}}_1{\supset}{\cdots}{\supset}{\mathcal{S}}_n$, where $S_q$ is the set of points where the Levi-form has nullity ${\geq}q$. We prove that ${\mathcal{S}}{_q}^{\prime}s$ are locally given as common zero sets of the coefficients $A_j$, $j=0,1,{\ldots},q-1$, of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$.

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References

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