Related papers: Uniform foliations with Reeb components

We realize the Reeb foliation of S^3 as a family of Legendrian submanifolds of the unit S^5 \subset C^3, Moreover we construct a deformation of the standard contact S^3 in S^5, via a family of contact submanifolds, into this realization.

A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit…

In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure…

We prove that there are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, fixed dimension $n\neq5$, and finite fundamental group, up to foliated diffeomorphism. In addition, we…

This paper compares two invariants of foliated manifolds which seem to measure the non-Hausdorffness of the leaf space: the transversal length on the fundamental group and the foliated Gromov norm on the homology. We consider foliations…

We study R-covered foliations of 3-manifolds from the point of view of their transverse geometry. For an R-covered foliation in an atoroidal 3-manifold M, we show that M-tilde can be partially compactified by a canonical cylinder S^1_univ x…

Let (M, F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we…

We prove that if $Y$ is the Gromov-Hausdorff limit of a sequence of compact manifolds, $M^n_i$, with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then $Y$ has a universal cover. We then show that, for $i$…

We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late…

We study the group of leafwise holomorphic smooth automorphisms of Reeb components of leafwise complex foliation which are obtained by a certain Hopf construction. In particular, in the case where the boundary holonomy is infinitely tangent…

We discuss various problems regarding the structure of the foliation of some foliated submanifolds S of C^n, in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates),…

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally…

Consider a singular Riemannian foliation (s.r.f for short) on a compact manifold. By successive blow-ups along the strata, we construct a regular Riemannian foliation on another compact Riemannian manifold and a desingularization map that…

We study the topological properties of the leaves of the singular foliation induced by a closed 1-form of Morse type on a compact orbifold. In particular, we establish criteria that characterize when all such leaves are compact, when they…

We prove that if F is a foliation of a compact manifold M with all leaves compact submanifolds, and the transverse saturated category of F is finite, then the leaf space M/F is compact Hausdorff. The proof is surprisingly delicate, and is…

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems…

Let $M$ be a closed orientable irreducible $3$-manifold such that $\pi_1(M)$ is left orderable. (a) Let $M_0 = M - Int(B^{3})$, where $B^{3}$ is a compact $3$-ball in $M$. We have a process to produce a co-orientable Reebless foliation…

We give a complete proof of the fact that a contact structure that is sufficiently close to a Reebless foliation is universally tight.

We study codimension one (transversally oriented) foliations $\fa$ on oriented closed manifolds $M$ having non-empty compact singular set $\sing(\fa)$ which is locally defined by Bott-Morse functions. We prove that if the transverse type of…

Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\mathcal{I}$ contains either a separatrix at $p$ or an invariant real…