Related papers: Low dimensional Singular Riemannian Foliations in …

Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-changing solutions to Yamabe type problems, which are constant…

Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to…

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by…

We study Lagrangian submanifolds foliated by (n-1)-spheres in R^2n for n>2. We give a parametrization valid for such submanifolds, and refine that description when the submanifold is special Lagrangian, self-similar or Hamiltonian…

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in product manifolds $M \times \R$, where $M$ is the hyperbolic plane, the Euclidean plane or the two dimensional sphere. The main…

Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ of on $G$. We then show that the foliation $\F$ is Riemannian…

This note explains a construction of a Poisson manifold whose symplectic foliation describes a deformation of a moduli space of meromorphic connections with unramified irregular singularities. In particular, this deformation of the moduli…

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 construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is…

In this article, we prove a series of integral formulae for a codimension-one foliated sub-Riemannian manifold, i.e., a Riemannian manifold $(M,g)$ equipped with a distribution ${\mathcal D}=T{\mathcal F}\oplus\,{\rm span}(N)$, where…

A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees…

We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such…

We construct a smooth codimension-one foliation on the five-sphere in which every leaf is a symplectic four-manifold and such that the symplectic structure varies smoothly. Our construction implies the existence of a complete regular…

We construct pairs of conformally equivalent isospectral Riemannian metrics $\phi_1 g$ and $\phi_2 g$ on spheres $S^n$ and balls $B^{n+1}$ for certain dimensions $n$, the smallest of which is $n=7$, and on certain compact simple Lie groups.…

We prove the nonexistence of a proper singular Riemannian foliation admitting section in compact manifolds of nonpositive curvature. Then we give a global description of proper singular Riemannian foliations admitting sections on Hadamard…

Let $(M,g)$ be an asymptotically flat Riemannian manifold of dimension $n\geq 3$ with positive mass. We give a short proof based on Lyapunov-Schmidt reduction of the existence of an asymptotic foliation of $(M, g)$ by stable constant mean…

We study left-invariant foliations $\mathcal{F}$ on Riemannian Lie groups $G$ generated by a subgroup $K$. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations…

In this paper, we prove that in the system of bending flows on the moduli space of polygons with fixed side lengths introduced by Kapovich and Millson, the singular fibers are isotropic homogeneous submanifolds. The proof covers the case…

We prove that, under reasonable conditions, odd co-dimension Riemannian foliations cannot occur in positively curved manifolds.

We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case there exists a one-to-one correspondence between algebras of…