Related papers: Some integrability conditions for almost K\"ahler …

We show that noncompact simply connected harmonic manifolds with volume density $\Theta_{p}(r) =\sinh ^{n-1} r$ is isometric to the real hyperbolic space and noncompact simply connected K\"{a}hler harmonic manifold with volume density…

It has been shown by Claire Voisin in 2003 that one cannot always deform a compact K\"ahler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an…

In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) $T$-flat quasi-Einstein manifolds with constant scalar curvature, where the…

We use some natural lifts defined on the cotangent bundle T*M of a Riemannian manifold (M,g) in order to construct an almost Hermitian structure (G,J) of diagonal type. The obtained almost complex structure J on T*M is integrable if and…

Let \((X,J,\omega)\) be a closed \(2n\)-dimensional almost K\"{a}hler manifold with negative sectional curvature. We prove that if the Nijenhuis tensor of the almost complex structure is sufficiently small, then the components of the…

We study rigidity on certain K\"ahler manifolds with nonnegative Ricci curvature. Among others things, we show that a complete noncompact K\"ahler surface with nonnegative Ricci curvature, Euclidean volume growth and quadratic curvature…

We classify compact almost-K\"ahler four manifolds with nonnegative biorthogonal curvature.

While small deformations of K\"ahler manifolds are K\"ahler too, we prove that the cohomological property to be $\mathcal{C}^\infty$-pure-and-full is not a stable condition under small deformations. This property, that has been recently…

Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is…

We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, SKT and astheno-K\"ahler metrics. We prove that the twistor spaces of compact hyperk\"ahler…

On 5-dimensional almost contact B-metric manifolds, the form of any K\"ahler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the…

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a…

We prove that compact K\"ahler manifolds whose sectional curvatures are close to 1/4-pinched have ratios of Chern numbers close to the corresponding ratios of a complex hyperbolic space form. We deduce that the Mostow-Siu surfaces (and…

First we confirm a conjecture asserting that any compact K\"ahler manifold $N$ with $\Ric^\perp>0$ must be simply-connected by applying a new viscosity consideration to Whitney's comass of $(p, 0)$-forms. Secondly we prove the projectivity…

We give a description of all $G$-invariant Ricci-flat K\"ahler metrics on the canonical complexification of any compact Riemannian symmetric space $G/K$ of arbitrary rank, by using some special local $(1,0)$ vector fields on $T(G/K)$. As…

For all complex dimensions n>=2, we construct complete Kaehler manifolds of bounded curvature and non-negative Ricci curvature whose Kaehler--Ricci evolutions immediately acquire Ricci curvature of mixed sign.

We show that any almost complex structure, positively tamed with $\omega$ on nearly K\"{a}hler 6-manifold $(M,g,J,\omega)$ is not integrable

There is considered a connection with skew symmetric torsion on a quasi-K\"ahler manifold with Norden metric. Some necessary and sufficient conditions are derived for the corresponding curvature tensor to be K\"ahlerian. In the case when…

We propose that under certain conditions heterotic string compactifications on half-flat and nearly-Kahler manifolds are equivalent. Based on this correspondence we argue that the moduli space of the nearly-Kahler manifolds under discussion…

In this paper, we prove that a gradient shrinking compact K\"ahler-Ricci soliton cannot have too large Ricci curvature unless it is K\"ahler-Einstein.