On isoparametric foliations of complex and quaternionic projective spaces

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(2026-09-25)except-m13.pdf (445.78 KB)
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URI: https://hdl.handle.net/10347/42915
E-ISSN: 1432-1823
DOI: 10.1007/s00209-025-03861-0

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2025

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Springer
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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.

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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00209-025-03861-0

Keywords

Polar foliation| Isoparametric foliation| FKM foliation| Singular Riemannian foliation| Homogeneous foliation| Complex projective space| Quaternionic projective space

Bibliographic citation

Domínguez-Vázquez, M., Kollross, A. On isoparametric foliations of complex and quaternionic projective spaces. Math. Z. 311, 68 (2025). https://doi.org/10.1007/s00209-025-03861-0

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The first author has been supported by the grants PID2022-138988NB-I00 funded by MI- CIU/AEI/10.13039/501100011033 and by ERDF, EU, and ED431C 2023/31 (Xunta de Galicia, Spain).

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Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)