On normal forms of singular Levi-flat real analytic hypersurfaces.

Let F( z) = Re( P( z)) + h.o.t be such that M = ( F = 0) defines a germ of real analytic Levi-flat at 0 ∈ ℂ, n ≥ 2, where P ( z) is a homogeneous polynomial of degree k with an isolated singularity at 0 ∈ ℂ and Milnor number µ. We prove that there exists a holomorphic change of coordinate ϕ such that ϕ( M) = ( Re( h) = 0), where h( z) is a polynomial of degree µ + 1 and j ( h) = P. [ABSTRACT FROM AUTHOR]