Tohoku Mathematical Journal
2018
September
SECOND SERIES VOL. 70, NO. 3

Tohoku Math. J.
70 (2018), 353-375

Title POLAR FOLIATIONS ON QUATERNIONIC PROJECTIVE SPACES

Author Miguel Domínguez-Vázquez and Claudio Gorodski

(Received January 28, 2016)
Abstract. We classify irreducible polar foliations of codimension $q$ on quaternionic projective spaces $\mathbb{H} P^n$, for all $(n,q)\neq(7,1)$. We prove that all irreducible polar foliations of any codimension (resp. of codimension one) on $\mathbb{H} P^n$ are homogeneous if and only if $n+1$ is a prime number (resp. $n$ is even or $n=1$). This shows the existence of inhomogeneous examples of codimension one and higher.

Mathematics Subject Classification. Primary 53C12; Secondary 53C35, 57S15.
Key words and phrases. Polar foliation, singular Riemannian foliation, $s$-representation, symmetric space, FKM-foliation, homogeneous foliation, quaternionic projective space.

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