Related papers: Lefschetz theorem for holomorphic one-forms on wea…

A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the…

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic…

We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that…

In this paper we study germs of holomorphic foliations, at the origin of the complex plane, tangent to Pfaffian hypersurfaces - integral hypersurfaces of real analytic 1-forms - satisfying the Rolle-Khovanskii condition. This hypothesis…

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert…

We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed.…

Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local…

We consider holomorphic mappings $H$ between a smooth real hypersurface $M\subset \bC^{n+1}$ and another $M'\subset \bC^{N+1}$ with $N\geq n$. We provide conditions guaranteeing that $H$ is transversal to $M'$ along all of $M$. In the…

Theorems of Barth-Lefschetz type describe restrictions on the topology of varieties of small codimension. R. Schoen and J. Wolfson, using Morse theory on a path space, have described a technique to prove theorems of this kind for complex…

We classify weakly Einstein submanifolds in space forms that satisfy Chen's equality. We also give a classification of weakly Einstein hypersurfaces in space forms that satisfy the semisymmetric condition. In addition, we discuss some…

If $X$ is a closed $2n$-dimensional aspherical manifold, i.e., the universal cover of $X$ is contractible, then the Chern-Hopf-Thurston conjecture predicts that $(-1)^n\chi(X)\geq 0$. We prove this conjecture when $X$ is a complex…

Let $\mathbb D$ be the unit disc in $\mathbb C$ and let $f:\mathbb D \to \mathbb C$ be a Riemann map, $\Delta=f(\mathbb D)$. We give a necessary and sufficient condition in terms of hyperbolic distance and horocycles which assures that a…

We prove an analogue of E. Levi's Continuity Principle for meromorphic mappings with values in arbitrary compact complex manifolds in place of the Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new extension method for…

We construct an irreducible holomorphic connection with SL(2,R)-monodromy on the trivial holomorphic vector bundle of rank two over a compact Riemann surface. This answers a question of Calsamiglia, Deroin, Heu and Loray in \cite{CDHL}.

One of the main purposes of this paper is to prove that on a complete K\"ahler manifold of dimension $m$, if the holomorphic bisectional curvature is bounded from below by -1 and the minimum spectrum $\lambda_1(M) \ge m^2$, then it must…

The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [Ka]. This theorem implies the conjecture of R. Stanley on the unimodularity of the generalized $h$-vector. In this paper we…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We study a special type of almost complex structures, called pure and full and introduced by T.J. Li and W. Zhang, in relation to symplectic structures and Hard Lefschetz condition. We provide sufficient conditions to the existence of the…

We give sharp conditions on a local biholomorphism $F:X \to \mathbb C^{n}$ which ensure global injectivity. For $n \geq 2$, such a map is injective if for each complex line $l \subset \mathbb C^{n}$, the pre-image $F^{-1}(l)$ embeds…

Let $(X, J)$ be a complex manifold with a non-degenerated smooth $d$-closed $(1,1)$-form $\omega$. Then we have a natural double complex $\overline{\partial}+\overline{\partial}^\Lambda$, where $\overline{\partial}^\Lambda$ denotes the…