Related papers: Strongly not relatives Kaehler manifolds

Let $\pi: \mathcal{X}^* \rightarrow B^*$ be an algebraic family of compact K\"ahler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\in \mathbb{C}$. Let $g_t$ be the unique K\"ahler-Einstein…

In this expository paper (Bourbaki talk) we survey results of Claire Voisin showing that there exist compact Kaehler manifolds which are not homeomorphic to any projective manifold.

We consider complete nearly K\"ahler manifolds with the canonical Hermitian connection. We prove some metric properties of strict nearly K\"ahler manifolds and give a sufficient condition for the reducibility of the canonical Hermitian…

We construct some families of complex structures on compact manifolds by means of normal almost contact structures (nacs) so that each complex manifold in the family has a non-singular holomorphic flow. These families include as particular…

This is the topological part of two papers on the cohomology of Kaehler groups. In this paper we show that if a linear duality group of dimension larger than 6 is the fundamental group of a compact Kaehler manifold then its second or its…

We show that if $M = X \times Y$ is the product of two complex manifolds (of positive dimensions), then $M$ does not admit any complete K\"ahler metric with bisectional curvature bounded between two negative constants. More generally, a…

We prove that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a Kaehler surface.

This paper is about non-holomorphic isometric immersions of Kaehler manifolds into Euclidean space $f\colon M^{2n}\to\R^{2n+p}$, $p\leq n-1$, with low codimension $p\leq 11$. In particular, it addresses a conjecture proposed by J. Yan and…

On a Kahler manifold there is a clear connection between the complex geometry and underlying Riemannian geometry. In some ways, this can be used to characterize the Kahler condition. While such a link is not so obvious in the non-Kahler…

A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on…

Any minimal model of a projective Hyperkaehler manifold is a projective Hyperkaehler manifold. As a consequence, moduli spaces of sheaves on a k3 that don't admit a symplectic resolution are not birational to Hyperkaehler manifolds.

Let $(M,I)$ be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (so-called Nijenhuis tensor) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it…

The structure of nearly K\"ahler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly K\"ahler manifold is…

For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations…

It is known that there exist no warped product semi-slant submanifolds in Kaehler manifolds \cite{Sahin}. Recently, Chen and Garay studied pointwise-slant submanifolds of almost Hermitian manifolds in \cite{CG} and obtained many new results…

We present new families of non-supersymmetric solutions of D=11 supergravity with non-relativistic symmetry, based on six-dimensional Kaehler-Einstein manifolds. In constructing these solutions, we make use of a consistent reduction to a…

In this note, we analyze the question of when will a complex nilmanifold have K\"ahler-like Strominger (also known as Bismut), Chern, or Riemannian connection, in the sense that the curvature of the connection obeys all the symmetries of…

In this paper we define strongly projectively flatness of holomorphic maps into the complex Grassmannian manifold, which is a kind of generalization of holomorphic maps into the complex projective space and prove a rigidity of equivariant…

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…

We follow our study of non-K\"ahler complex structures on $R^4$ that we defined in a previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their…