A non-existence theorem for Morse type holomorphic foliations of codimension one transverse to spheres

2008/11/12 by Toshikazu Ito, Bruno Scardua, Ito, Toshikazu +2
Mathematics · #32S65 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.CV #math.DS #msc:32S65

paper · pdf · doi:10.48550/arxiv.0811.1818

arxiv created 2008/11/12 · openalex publication_date 2008/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a Morse type codimension one holomorphic foliation is not transverse to a sphere in the complex affine space. Also we characterize the variety of contacts of a linear foliation with concentric spheres.

Related

• Morse foliations of codimension one on the sphere S³
• Transversely projective holomorphic foliations with singularities
• Codimension one foliations with Bott-Morse singularities I
• Foliations with Morse singularities
• Compact leaves of codimension one holomorphic foliations on projective manifolds