Related papers: Foliated vector bundles and riemannian foliations

We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.

Let $(M,\omega)$ be a symplectic manifold endowed with a agrangian foliation ${\cal L}$, it has been shown by Weinstein [16] hat the symplectic structure of $M$ defines on each leaf of ${\cal L}$, connection which curvature and torsion…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

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.

We prove that, for 3 < m < n-1, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension n is birational to the Hilbert scheme of the degeneracy loci of m global sections of Omega(2),…

Let $\FF$ be a codimension one foliation on a closed manifold $M$ which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.

We prove a version of Weyl's Law for the basic spectrum of a closed singular Riemannian foliation $(M,\mathcal{F})$ with basic mean curvature. In the special case of $M=\mathbb{S}^n$, this gives an explicit formula for the volume of the…

This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic…

Given a Lie groupoid, we can form its orbit space, which carries a natural diffeology. More generally, we have a quotient functor from the Hilsum-Skandalis category of Lie groupoids to the category of diffeological spaces. We introduce the…

For non-degenerate surfaces in $R^4$, a distinguished transversal bundle called affine normal plane bundle was proposed in [Nomizu-Vrancken]. Lagrangian surfaces have remarkable properties with respect to this normal bundle, like for…

The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\to E\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable connections in the bundle $E\to…

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…

Given a cooriented branched surface $\mathcal B$ fully carrying a foliation $\mathcal F$, we use the dual graph of $\mathcal B$ to define a simplicial 1-cycle $\Gamma_m(\mathcal B)$ representing the Poincar\'e dual of the Euler class of…

Irreducible isoparametric foliations of arbitrary codimension q on complex projective spaces CP^n are classified, except if n=15 and q=1. Remarkably, there are noncongruent examples that pull back under the Hopf map to congruent foliations…

In this paper, we use the methods of subriemannian geometry to study the dual foliation of the singular Riemannian foliation induced by isometric Lie group actions on a complete Riemannian manifold M. We show that under some conditions, the…

Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves…

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 call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian…

We begin by studying the Riemannian geometry of the tangent Lie group $TG$ associated with a Lie group $G$ whose commutator subgroup is two-dimensional, equipped with the lift of a left-invariant Riemannian metric on $G$. We establish the…

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…