A Morse-Bott normal form for real analytic Levi-flat hypersurfaces

2025/11/02 by Arturo Fernández‐Pérez, Fernández-Pérez, Arturo, Gustavo Marra +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2511.01088

openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

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.

Citations

• Codimension one foliations with Bott-Morse singularities I

Related

• Pull-back of singular Levi-flat hypersurfaces
• Chow's theorem for real analytic Levi-flat hypersurfaces
• Normal forms of real hyepersurfaces with nondegenerate Levi form
• Singular Levi-flat hypersurfaces and codimension one foliations
• Levi-flats in \mathbbCPⁿ: a survey for nonexperts