A normal form for a real 2-codimensional submanifold in $\mathbb{C}^{N+1}$ near a CR singularity

@article{Burcea2011ANF,
  title={A normal form for a real 2-codimensional submanifold in \$\mathbb\{C\}^\{N+1\}\$ near a CR singularity},
  author={Valentin Burcea},
  journal={arXiv: Complex Variables},
  year={2011}
}
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29 Citations
Highly Influential Citations
1
Background Citations
4
Methods Citations
4
Results Citations
1

29 Citations

Real submanifolds of maximum complex tangent space at a CR singular point, I
We study a germ of real analytic n-dimensional submanifold of $${\mathbf {C}}^n$$Cn that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions, we show its…
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This paper is a sequel to our previous paper \cite{TS2}. We extend the result on the behavior of the quadratic part of normal forms up to the quadratic part of small $\mathcal{C}^{2}$-perturbations…
Flattening a non-degenerate CR singular point of real codimension two
This paper continues the previous studies in two papers of Huang–Yin [HY16,HY17] on the flattening problem of a CR singular point of real codimension two sitting in a submanifold in $${{\mathbb…
Convergent normal form and canonical connection for hypersurfaces of finite type in $\mathbb C^2$
We study the holomorphic equivalence problem for finite type hypersurfaces in $\mathbb C^2$. We discover a geometric condition, which is sufficient for the existence of a natural convergent normal…
On Complex Points of Codimension 2 Submanifolds
In this paper we study the structure of complex points of codimension 2 real submanifolds in complex $$n$$n-dimensional manifolds. We show that the local structure of complex points up to isotopy…
Real submanifolds of maximum complex tangent space at a CR singular point, II
We study a germ of real analytic n-dimensional submanifold of C that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the…
Convergent normal form and canonical connection for hypersurfaces of finite type in C2
NORMAL FORMS FOR CR SINGULAR CODIMENSION TWO LEVI-FLAT SUBMANIFOLDS
Real-analytic Levi-flat codimension two CR singular submanifolds are a natural generalization to C m , m > 2, of Bishop surfaces in C 2 . Such submanifolds for example arise as zero sets of…
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