Related papers: The Frolicher-type inequalities of foliations

In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness…

Starting with a concise review of quaternionic geometry and quaternionic K{\"a}hler manifolds, we define a transversely quaternionic K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of…

Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation which satisfies the transverse hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic…

We prove inequalities relating the degrees of holomorphic distributions and of holomorphic foliations forming a flag on $\mathbb{P}^n$. Such inequalities are inspired by the so called Poincar\'e problem for foliations.

In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.

Let $\cal{F}$ be a regular codimension 1 holomorphic foliation on a compact K\" ahler manifold. One assumes in addition that $\cal{F}$ possesses a transverse invariant positive current. The aim of this paper is to establish the following…

We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K.~Pak, "Transversal harmonic theory for transversally symplectic flows", J. Aust.…

In this paper, we study the twisted basic Dolbeault cohomology and transverse hard Lefschetz theorem on a transverse Kahler foliation. And we give some properties for $\Delta_\kappa$-harmonic forms and prove the Kodaira-Serre type duality…

We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…

We study properties of the mean curvature one-form and its holomorphic and antiholomorphic cousins on a transverse K\"ahler foliation. If the mean curvature of the foliation is automorphic, then there are some restrictions on basic…

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…

Let F be a K\"ahler foliation on a compact Riemannian manifold M. we study the properties of infinitesimal automorphisms on (M,F), and in particular we concentrate on the transversal conformal field, transversal projective field and…

We prove a Fr\"olicher-type inequality for a compact generalized complex manifold $M$, and show that the equality holds if and only if $M$ satisfies the generalized $\partial\bar{\partial}$-Lemma. In particular, this gives a unified proof…

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…

A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is studied. It seems unknown if there is a real foliation with non-trivial FLK class. In this article, we show some…

We prove that the foliated Euler caracteristic classifies amenable measured foliations up to those defined by ergodic actions of the euclidian plane.

We propose an inequality between the longitudinally polarized density and the transversity of a quark in a nucleon. This inequality, whose validity is limited to very small scales, is based on considerations about Lorentz transformations…

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.