Related papers: Polar foliations and isoparametric maps

We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.

We give a classification of pairs (F, f) where F is a holomorphic foliation on a projective surface and f is a non-invertible dominant rational map preserving F. We prove that both the map and the foliation are integrable in a suitable…

We study foliations $\mathcal{F}$ on Hirzebruch surfaces $S_\delta$ and prove that, similarly to those on the projective plane, any $\mathcal{F}$ can be represented by a bi-homogeneous polynomial affine $1$-form. In case $\mathcal{F}$ has…

In this article, we show that for any deformation of analytic foliations, there exists a maximal analytic singular foliation on the space of parameters along the leaves of which the deformation is integrable.

A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the…

A point-shift $F$ maps each point of a point process $\Phi$ to some point of $\Phi$. For all translation invariant point-shifts $F$, the $F$-foliation of $\Phi$ is a partition of the support of $\Phi$ which is the discrete analogue of the…

For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a…

It is proved that any (repetitive) Riemannian manifold of bounded geometry can be realized as a leaf of some (minimal) Riemannian matchbox manifold without holonomy. Our methods can be adapted to achieve Cantor transversals or a prescribed…

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction $\sigma|_Y$ of the holomorphic symplectic form induces a rank one foliation on Y. We investigate situations where this foliation has compact…

We investigate under which assumptions an orientable pseudo-Riemannian geodesic foliations by circles is generated by an $S^1$-action. We construct examples showing that, contrary to the Riemannian case, it is not always true. However, we…

We consider the Grassmann graphs and dual polar graphs over the same finite field and show that, up to graph automorphism, for every dual polar graph there is the unique isometric embedding in the corresponding Grassmann graph.

We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$. By combining differential geometry and analysis techniques, we establish the…

Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine the maximal value that $|\mbox{aut}(\mathcal{F})|$ can…

Let $M$ be a smooth manifold and let $\F$ be a codimension one, $C^\infty$ foliation on $M$, with isolated singularities of Morse type. The study and classification of pairs $(M,\F)$ is a challenging (and difficult) problem. In this…

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter…

The main result of this paper is that a polar action on a compact irreducible homogeneous Kaehler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.

In this paper, we first prove that any closed simply connected 4-manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4-manifolds: $\mathbb{S}^4$,…

R. Zimmer proved that, on a compact manifold, a foliation with a dense leaf, a suitable leafwise Riemannian symmetric metric and a transverse Lie structure has arithmetic holonomy group. In this work we improve such result for totally…

In this paper we characterise with the matrix the complete flag of riemannian extension (see d\'efinition) on a riemannian compact manifold whose metric is bundlelike for any foliation F_{s} of this flag. This study show us that a foliation…

We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or K\"ahler space.