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

TL;DR

This paper proves that Morse type codimension one holomorphic foliations cannot be transverse to spheres in complex affine space and characterizes their contact with concentric spheres.

Contribution

It establishes a non-existence theorem for such foliations and provides a detailed characterization of their contact with spheres.

Findings

Morse type foliations are not transverse to spheres in complex affine space.

Characterization of contact points between linear foliations and concentric spheres.

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.