相关论文: Singular Riemannian Foliations with Sections

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…

Hiss and Szczepa\'nski proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean lattice associated with the manifold via the first…

We extend the classical theory of sphere theorems to the transverse geometry of Riemannian foliations. In this setting, we establish transverse analogues of the Grove-Shiohama diameter sphere theorem and of the Berger-Klingenberg…

Let $\Gamma$ be a nondegenerate geodesic in a compact Riemannian manifold $M$. We prove the existence of a partial foliation of a neighbourhood of $\Gamma$ by CMC surfaces which are small perturbations of the geodesic tubes about $\Gamma$.…

In this paper, two sequences of minimal isoparametric hypersurfaces are constructed via representations of Clifford algebras. Based on these, we give estimates on eigenvalues of the Laplacian of the focal submanifolds of isoparametric…

We identify a class of singular algebraic foliations whose leaves through singular points retain regularity. The proof consists in showing existence of residual gerbes for certain formal stacks, which do not enjoy smooth presentations. As…

We prove Wadsley's theorem for foliations by closed non-lightlike geodesics. As an application we show that every pseudo-Riemannian and non-Riemannian 2-mainfold, all of whose time- or spacelike geodesics are closed, is diffeomorphic to…

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.

An equifocal submanifold M of a symmetric space N of compact type induces a foliation with singular leaves on N. In this paper we will show how to reconstruct the equifocal foliation starting from one of the singular leaves, the so-called…

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures…

We show that every topological surface lamination of a 3-manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2…

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions…

In this paper we investigate the mean curvature flow (MCF) of a regular leaf of a closed generalized isoparametric foliation as initial datum, generalizing previous results of Radeschi and first author. We show that, under bounded curvature…

At the end of 1960-ths Yu.S.Ilyashenko stated the problem: is it true that for any one-dimensional holomorphic foliation with singularities on a Stein manifold leaves intersecting a transversal disc can be uniformized so that the…

In this survey we present classical results on methods to use group actions to collapse manifolds to the orbit spaces while keeping some control on the curvature, and recent extensions of these constructions to the setting of singular…

The aim of this paper is to study codimension one foliations on rational homogeneous spaces, with a focus on the moduli space of foliations of low degree on Grassmannians and cominuscule spaces. Using equivariant techniques, we show that…

The $\text{PSL}(4,\mathbb{R})$ Hitchin component of a closed surface group $\pi_1(S)$ consists of holonomies of properly convex foliated projective structures on the unit tangent bundle of $S$. We prove that the leaves of the…

We prove localization and integration formulas for the equivariant basic cohomology of Riemannian foliations. As a corollary we obtain a Duistermaat-Heckman theorem for transversely symplectic foliations.

We prove that any holomorphic codimension 1 foliation on the complex projective plane has at most one singular point up to the action of an ad-hoc birational self map of the complex projective plane into itself. Consequently, any algebraic…