A Morse-Bott normal form for real analytic Levi-flat hypersurfaces
Abstract
We prove the existence of a normal form for a real-analytic Levi-flat hypersurface defined by the vanishing of the real part of a holomorphic function with a Morse-Bott singularity. As a consequence, we recover the Burns-Gong normal form for Levi-flat hypersurfaces with generic Morse singularities and provide a new normal form for a certain class of real analytic quadratic Levi-flat hypersurfaces.
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