Nullity of the Levi-form and the associated subvarieties for pseudo-convex CR structures of hypersurface type
Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 169-178
Published online 2019 Jan 31
Kuerak Chung, Chong-Kyu Han
Korea Institute for Advanced Study; Seoul National University
Abstract : Let $M^{2n+1}$, $n\ge 1$, be a smooth manifold with a pseudo-convex 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 $\mathcal S_q$ is the set of points where the Levi-form has nullity $\ge q$. We prove that $\mathcal S_q$'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 $A_j$.
Keywords : CR structure, invariant subvarieties, nullity of Levi-form, complex submanifolds
MSC numbers : Primary 32V05, 53A55; Secondary 32V25, 35N10
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