Hypersurfaces through higher-codimensional submanifolds of \(\mathbb{C}^n\) with preserved Levi-kernel
Let \(S\) be a submanifold of a complex manifold \(X,\) and assume that \(S\) is generic, i.e. \(TS+\sqrt{-1}TS=TX\). The author shows that one may construct a hypersurface \(M\supset S\) with Levi-form \(L_M\) with as many negative (or positive) eigenvalues as \(L_S\), the Levi-form of \(S\), at a prescribed conormal. When \(\text{rank }L_S\) is constant, he shows that \(M\) can be found such that \(L_M\) and \(L_S\) have the same number of negative eigenvalues at any common conormal, and in this last case, he discusses the relation between complex submanifolds of \(S\) whose tangent plane belongs to the null-space of \(L_S\) and complex submanifolds of \(\dot T_S^*X\). He finally applies this construction to propagation of micro-analyticity of CR-hyperfunctions along complex, \(L_S\)-null, curves.
scientific article; zbMATH DE number 1123742