Related papers: Smooth foliations on homogeneous compact K\"ahler …

We give a complete classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient manifold. The results are analogues of Haefliger's classification of foliations on open manifold.

We investigate the stability of fibers of coisotropic fibrations on holomorphic symplectic manifolds and generalize Voisin's result on Lagrangian subvarieties to this framework. We present applications to the moduli space of holomorphic…

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 will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of…

We study those real $\mathcal{C}^\infty$ foliations in complex surfaces whose leaves are holomorphic curves. The main motivation is to try and understand these foliations in neighborhoods of curves: can we expect the space of foliations in…

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of…

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the…

Let $(M^n, g)$ be a compact K\"ahler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact K\"ahler manifold $N^k$ with $c_1 < 0$. This confirms a…

We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger…

In this paper we provide a positive answer to a conjecture due to A. J. Di Scala, A. Loi, H. Hishi (see [3, Conjecture 1]) claiming that a simply-connected homogeneous K\"ahler manifold M endowed with an integral K\"ahler form $\mu\omega$,…

Compact K\"ahler solvmanifolds are classified up to biholomorphism. A proof of a conjecture Benson and Gordon, that completely solvable compact K\"ahler solvmanifolds are tori is deduced from this. The main ingredient in the proof is a…

We show the existence of a compact K\"ahler manifold which does not fit in a proper flat family over an irreducible base with one projective (possibly singular) fiber. We also give a topological version of this statement. This strengthens…

We investigate a class of locally conformal almost K\"ahler structures and prove that, under some conditions, this class is a subclass of almost K\"ahler structures. We show that a locally conformal almost K\"ahler manifold admits a…

In his work on birational classification of foliations on projective surfaces, Brunella showed that every regular foliation on a rational surface is algebraically integrable with rational leaves. This led Touzet to conjecture that every…

Fibrations methods which were previously used for complex homogeneous spaces and CR-homogenous spaces of special types ([HO1], [AHR], [HR],[R]}) are developed in a general framework. These include the $\lie g$-anticanonical fibration in the…

We prove that any compact homogeneous locally conformally K\"ahler manifold has parallel Lee form.

It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the fact that codimension one foliations of complex manifolds are necessarily locally Monge-Amp\`ere foliations and that…

A tractable definition of the homogeneous nearly K\"ahler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$,…

In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For…

We investigate degenerate special-Hermitian metrics on compact complex manifolds, in particular, degenerate K\"ahler and locally conformally K\"ahler metrics on special classes of non-K\"ahler manifolds.