Related papers: Compact complex manifolds whose complement of an a…

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…

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the…

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…

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra $\slt$ on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding…

We show that a compact K\"ahler manifold $M$ containing a smooth connected divisor $D$ such that $M \setminus D$ is a homology cell, e.g., contractible, must be projective space with $D$ a hyperplane, provided $\dim M \not \equiv 3 \pmod…

We extend to metric compact mapping tori a splitting result for coK\"ahler manifolds. In particular, we prove that a compact Vaisman manifold is finitely covered by the product of a Sasakian manifold and a circle.

On an almost complex manifold, a quasi-K\"{a}hler metric, with canonical connection in the c-projective class of a given minimal complex connection, is equivalent to a non-degenerate solution of the c-projectively invariant metrizability…

In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$…

We prove abundance for a minimal Kaehler threefold which is not both simple and non-Kummer. Recall that a variety is simple if there is no compact subvariety of positive dimension through a sufficiently general point . Furthermore we prove…

In this paper, we establish the proof of general Kastler-Kalau-Walze type theorems for conformal perturbations of dirac Operators on even dimensional compact manifolds with (respectively without) boundary.

This paper illustrates the notion of a Cartan subalgebra in a C*-algebra through a number of examples and counterexamples. Some of these examples have a geometrical flavour and are related to orbifolds and non-Hausdorff manifolds.

The central topic of this thesis is the study of some properties of a class of complex compact manifolds~: Moishezon manifolds. In the first part, we generalize J.-P. Demailly's holomorphic Morse inequalities to the case of a line bundle…

We study the Dirichlet problem for complex Monge-Ampere equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in the flat case. We…

We prove that any nilpotent regular covering over a compact K\"ahler surface is holomorphically convex if it does not have two ends. Furthermore, we show that the Malcev covering of any compact K\"ahler manifold has at most one end.

In this note we give a simplified proof of a recent result of X.X. Chen, which together with work of G. Szekelyhidi implies that on a sufficiently small deformation of a polarized constant scalar curvature Kahler manifold the K-energy has a…

It is shown that a compact $n$-dimensional K\"ahler manifold with $\frac{n}{2}$-positive Calabi curvature operator has the rational cohomology of complex projective space. For even $n,$ this is sharp in the sense that the complex quadric…

We give a classification of compact conformally Kahler Einstein-Weyl manifolds whose Ricci tensor is hermitian.

We study Kahler surfaces with harmonic anti-selfdual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including…

Let $M$ be an irreducible holomorphically symplectic manifold. We show that all faces of the Kahler cone of $M$ are hyperplanes $H_i$ orthogonal to certain homology classes, called monodromy birationally minimal (MBM) classes. Moreover, the…

We show that on a compact K\"ahler manifold all real $(1,1)$-classes admitting solutions to the supercritical deformed Hermitian-Yang-Mills equation form a both open and closed subset of those which satisfy the numerical condition proposed…