On isoparametric foliations of complex and quaternionic projective spaces

TL;DR

This paper completes the classification of isoparametric foliations in complex and quaternionic projective spaces by analyzing their relation to foliations of spheres via Hopf fibrations.

Contribution

It provides the final classification of inhomogeneous isoparametric foliations in these spaces, solving previously open cases through projection methods.

Findings

Classification of all isoparametric foliations in complex projective spaces.

Classification of all isoparametric foliations in quaternionic projective spaces.

Resolution of the last open cases in the classification problem.

Abstract

We conclude the classification of isoparametric (or equivalently, polar) foliations of complex and quaternionic projective spaces. This is done by investigating the projections of certain inhomogeneous isoparametric foliations of the 31-sphere under the respective Hopf fibrations, thereby solving the last remaining open cases.