Related papers: Curvature of quaternionic K\"ahler manifolds with …
The K\"ahler cone of a compact K\"ahler manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We give cohomological expressions for the Levi-Civita connection and curvature tensor of this…
We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…
We study symmetry properties of quaternionic K\"ahler manifolds obtained by the HK/QK correspondence. To any Lie algebra $\mathfrak{g}$ of infinitesimal automorphisms of the initial hyper-K\"ahler data we associate a central extension of…
In this article, we examine the behavior of the Riemannian and Hermitian curvature tensors of a Hermitian metric, when one of the curvature tensors obeys all the symmetry conditions of the curvature tensor of a K\"ahler metric. We will call…
We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with…
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…
The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…
On an almost Hermitian manifold, we have two Hermitian scalar curvatures with respect to any canonical Hermitian connection defined by P. Gauduchon. Explicit formulas of these two Hermitian scalar curvatures are obtained in terms of…
We express characteristic numbers of compact hyperk\"ahler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by…
We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space $\Hnn$ and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in $\Hnn$ is…
We introduce the notion of tame $\rho$-quaternionic manifold that permits the construction of a finite family of $\rho$-connections, significant for the geometry involved. This provides, for example, the following: (1) a new simple global…
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…
We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then the manifold has a canonical…
A classification theorem for nearly K\"ahler manifolds of constant antiholomorphic sectional curvature is proved.
We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…
A tensor invariant is defined on a paraquaternionic contact manifold in terms of the curvature and torsion of the canonical paraquaternionic connection involving derivatives up to third order of the contact form. This tensor, called…
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…
In this manuscript we study natural symmetries of Kaehler manifolds: constant holomorphic sectional curvature Kaheler manifolds, semisymmetric Kaehler manifolds and holomorphically pseudosymmetric Kaehler manifolds. We get characterization…
A type of almost contact hypersurfaces with Norden metric of a Kaehler manifold with Norden metric is considered. The curvature tensor and the special sectional curvatures are characterized. The canonical connection on such manifolds is…
Using quaternionic Feix--Kaledin construction we provide a local classification of quaternion-K\"ahler metrics with a rotating $S^1$-symmetry with the fixed point set submanifold $S$ of maximal possible dimension. For any K\"ahler manifold…