# 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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## References

SHOWING 1-10 OF 38 REFERENCES
Real analytic manifolds in ${\mathbb{C}}^n$ with parabolic complex tangents along a submanifold of codimension one
• Mathematics
• 2009
We will classify n-dimensional real submanifolds in C" which have a set of parabolic complex tangents of real dimension n-1. All such submanifolds are equivalent under formal biholomorphisms. We will
Boundary problem for Levi flat graphs
• Mathematics
• 2009
In an earlier paper the authors provided general conditions on a real codimension 2 submanifold $S\subset C^{n}$, $n\ge 3$, such that there exists a possibly singular Levi-flat hypersurface $M$
Analytic Normal Form for CR Singular Surfaces in C3
A real analytic surface inside complex 3-space with an isolated, non-degenerate complex tangent is shown to be holomorphically equivalent to a fixed real algebraic variety. The analyticity of the
CR singularities of real fourfolds in ℂ3
CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation
Normal forms and biholomorphic equivalence of real hypersurfaces in C^3
We consider the problem of describing the local biholomorphic equivalence class of a real-analytic hypersurface $M$ at a distinguished point $p_0\in M$ by giving a normal form for such objects. In
A Codimension Two CR Singular Submanifold That Is Formally Equivalent to a Symmetric Quadric
• Mathematics
• 2008
Let () be a real analytic submanifold defined by an equation of the form: w=| z| 2 + O(| z| 3 ), where we use for the coordinates of . We first derive a pseudonormal form for M near 0. We then use it
On an $n$-manifold in $\mathbf{C}^n$ near an elliptic complex tangent
In this paper, we will be concerned with the local biholomorphic properties of a real n-manifold M in C. At a generic point, such a manifold basically has the nature of the standard R in C. Near a
Nowhere minimal CR submanifolds and Levi-flat hypersurfaces
A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given
CR singularities of real threefolds in ℂ4
CR singularities of real threefolds in C4 are classified by using holomorphic coordinate changes to transform the quadratic part of the real defining equations into one of a list of normal forms. In
Unfolding CR Singularities
A notion of unfolding, or multi-parameter deformation, of CR singularities of real submanifolds in complex manifolds is proposed, along with a definition of equivalence of unfoldings under the action