Polar foliations on quaternionic projective spaces
Copyright policy )Polar foliations on quaternionic projective spaces
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.
Compact Lie groups of differentiable transformations, Mathematics - Differential Geometry, quaternionic projective space, 53C12 (Primary), 53C35, 57S15 (Secondary), 53C12, $s$-representation, homogeneous foliation, 53C35, symmetric space, singular Riemannian foliation, polar foliation, FKM-foliation, Differential Geometry (math.DG), Foliations (differential geometric aspects), FOS: Mathematics, Differential geometry of symmetric spaces, 57S15
Compact Lie groups of differentiable transformations, Mathematics - Differential Geometry, quaternionic projective space, 53C12 (Primary), 53C35, 57S15 (Secondary), 53C12, $s$-representation, homogeneous foliation, 53C35, symmetric space, singular Riemannian foliation, polar foliation, FKM-foliation, Differential Geometry (math.DG), Foliations (differential geometric aspects), FOS: Mathematics, Differential geometry of symmetric spaces, 57S15
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