Related papers: Kaehler structures on spin 6-manifolds

An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus…

We determine an explicit expression for the Ricci tensor of a K-manifold, that is of a compact Kaehler manifold M with vanishing first Betti number, on which a semisimple group G of biholomorphic isometries acts with an orbit of codimension…

We obtain a locally symmetric Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the cotangent bundle, in the…

We consider non-Kaehler compact complex manifolds which are homogeneous under the action of a compact Lie group of biholomorphisms and we investigate the existence of special (invariant) Hermitian metrics on these spaces. We focus on a…

The underlying complex structure of an ALE K\"ahler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE K\"ahler…

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

The space of shapes of a polyhedron with given total angles less than 2\pi at each of its n vertices has a Kaehler metric, locally isometric to complex hyperbolic space CH^{n-3}. The metric is not complete: collisions between vertices take…

We recently constructed examples of compact Kaeler manifolds which do not have the homotopy type of a projective complex manifold. They were however obtained by blowing-up certain complex tori, which are themselves deformation equivalent to…

This is the geometric part of two papers on the cohomology of Kaehler groups. Using non-Abelian Hodge theory we show that if a finitely presented group with an unbounded complex linear morphism is the fundamental group of a compact Kaehler…

We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical…

Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We offer a new approach to this field of study via Rational…

We first construct closed spherical CR manifolds of dimension at least five having non-trivial first Chern class with real coefficients. We next prove a constraint on Chern classes with real coefficients of (not necessarily closed)…

Let $M^n$ be a compact K$\ddot{a}$hler manifold with almost nonnegative Ricci curvature and nonzero first Betti number. We show that the holomorphic Euler number of $M^n$ vanishes, which gives a new obstruction for compact complex manifolds…

We show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy…

We ask about the simply connected compact smooth 6-manifolds which can support structures of Calabi-Yau threefolds. In particular, we study the interesting case of Calabi-Yau threefolds $X$ with second betti number 3. We have a cup-product…

We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…

We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to the existence of flat structures, confirming an old…

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$, with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed $n$-manifold. We further investigate the structure of generalized…