Related papers: On nearly K\"{a}hler and K\"{a}hler-Codazzi type m…
We show that the Weyl structure of an almost-Hermitian Weyl manifold of dimension at least 6 is trivial if the associated curvature operator satisfies the Kaehler identity. Similarly if the curvature of an almost para-Hermitian Weyl…
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…
The aim of this paper is to classify compact Kahler manifolds with quasi-constant holomorphic sectional curvature.
In this paper, we introduce the notions of pseudo-Riemannian, para-Hermitian and para- Kahler structures on hom-Lie algebras. In addition, we present the characterization of these structures. Also, we provide an example including these…
We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the…
We obtain a classification theorem for non Kaehler nearly Kaehler manifolds with vanishing Bochner curvature tensor (introduced by Tricerri and Vanhecke).
Motivated by a recent work of Chen-Zheng [8] on Strominger space forms, we prove that a compact Hermitian surface with pointwise constant holomorphic sectional curvature with respect to a Gauduchon connection $\nabla^t $ is either K\"ahler,…
In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of…
In this paper, we study a special type of compact Hermitian manifolds that are Strominger K\"ahler-like, or SKL for short. This condition means that the Strominger connection (also known as Bismut connection) is K\"ahler-like, in the sense…
We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric,…
In this paper, by introducing a notion of local quasi holomorphic frame, we obtain a curvature formula for almost Hermitian manifolds which is similar to that of Hermitian manifolds. Moreover, as applications of the curvature formula, we…
On a class of compact Hermitian manifolds including compact K\"{a}hler manifolds, we prove that the the relative non-pluripolar product is always well-defined. We also prove the monotonicity of the relative non-pluripolar product in terms…
The notions of coK\"{a}hler manifolds and 3-cosymplectic manifolds are odd-dimensional analogues of the ones of K\"{a}hler manifolds and hyperK\"{a}hler manifolds, respectively. In this paper, we obtain reduction theorems of coK\"{a}hler…
The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.
We consider the reduced twistor space $Z$ of an almost Hermitian manifold $M$, after O'Brian and Rawnsley (Ann. Global Anal. Geom., 1985). We concentrate on dimension 6. This space has a natural almost complex structure $\mathcal J$…
We study the pseudoriemannian geometry of almost parahermitian manifolds, obtaining a formula for the Ricci tensor of the Levi-Civita connection. The formula uses the intrinsic torsion of an underlying SL(n,R)-structure; we express it in…
In this paper we study invariant almost Hermitian geometry on generalized flag manifolds which the isotropy representation decompose into two or three irreducible components. We will provide a classification of such flag manifolds admitting…
In this paper, we show several rigidity results for harmonic $(p,q)$-forms in complete K\"{a}hler manifolds. We also give several applications to study non-compact K\"{a}hler manifolds with parallel Bochner tensor or quaternion K\"{a}hler…
We classify compact almost-K\"ahler four manifolds with nonnegative biorthogonal curvature.
We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost K\"ahler manifolds. We give an explicit non-compact example of an Einstein almost cok\"ahler manifold that is not cok\"ahler. We prove that compact…