Related papers: A splitting theorem for compact Vaisman manifolds

We introduce a notion of K-semistability for Sasakian manifolds. This extends to the irregular case the orbifold K-semistability of Ross-Thomas. Our main result is that a Sasakian manifold with constant scalar curvature is necessarily…

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…

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A…

We prove a warped product splitting theorem for manifolds with Ricci curvature bounded from below in the spirit of [Croke-Kleiner, \emph{Duke Math.\;J}.\;(1992)], but instead of asking that one boundary component is compact and mean-convex,…

A contact manifold $M$ can be defined as a quotient of a symplectic manifold $X$ by a proper, free action of $\R^{>0}$, with the symplectic form homogeneous of degree 2. If $X$ is, in addition, Kaehler, and its metric is also homogeneous of…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over…

Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are…

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold…

Weak contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak, allowed us to take a new look at the theory of contact…

We study compact toric strict locally conformally K\"ahler manifolds. We show that the Kodaira dimension of the underlying complex manifold is $-\infty$ and that the only compact complex surfaces admitting toric strict locally conformally…

A long-term project is to construct a complete Calabi-Yau metric on the complement of the anticanonical divisor in a compact K\"ahler manifold $\oM$. We focus on the case where this smooth divisor has multiplicity 2 and is itself a compact…

We show that for $n>2$ a compact locally conformally K\"ahler manifold $(M^{2n},g,J)$ carrying a non-trivial parallel vector field is either Vaisman, or globally conformally K\"ahler, determined in an explicit way by some compact K\"ahler…

We construct explicitly a finite cover of the moduli stack of compact Riemann surfaces with a given group of symmetries by a smooth quasi-projective variety.

We show that the contact reduction can be specialized to Sasakian manifolds. We link this Sasakian reduction to K\"ahler reduction by considering the K\"ahler cone over a Sasakian manifold. We present examples of Sasakian manifolds obtained…

As proven in a celebrated theorem due to Vaisman, pure locally conformally K\"ahler metrics do not exist on compact K\"ahler manifolds. In a previous paper, we extended this result to the singular setting, more precisely to K\"ahler spaces…

A solvmanifold is a compact differentiable manifold M on which a connected solvable Lie group G acts transitively. As the main result, we will see, applying a result of Arapura and Nori on solvable Kaehler groups and some of the author's…

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…

We give an overview of some recent results in hypersymplectic and para-quaternionic Kahler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of…

Recent renewed interest in Sasakian manifolds is due mainly to the fact that they can provide examples of generalized Einstein manifolds, manifolds which are of great interest in mathematical models of various aspects of physical phenomena.…