Remarks on astheno-Kahler manifolds, Bott-Chern and Aeppli cohomology groups
We provide a new cohomological obstruction to the existence of astheno-Kahler metrics, and study relevant examples.
math.DG↗
arXiv subjects
Ionut Chiose
Publications and source records attributed to Ionut Chiose.
Positive currents on non-kählerian surfaces, II
We present some properties of positive closed currents of type $(1,1)$ on compact non-kählerian surfaces related to our previous study of these objects started in \cite{ChiTo2}.
math.CV↗
Balanced metrics on uniruled manifolds
We show that an $n-$dimensional Moishezon manifold is uniruled if and only if it supports a balanced metric $ω^{n-1}$ of positive total scalar Chern curvature. A similar statement also holds true for class $\mathcal C$ manifolds of dimension three.
math.DG↗
On the invariance of the total Monge-Ampere volume of Hermitian metrics
In this note, we describe the Hermitian metrics that leave the total Monge-Ampere volume invariant. In particular, we give several characterizations of the Hermitian metrics which satisfy the comparison principle for the complex Monge-Ampere operator
math.DG↗
Balanced Manifolds and SKT Metrics
The equality between the balanced and the Gauduchon cones is discussed in several situations. In particular, it is shown that equality does not hold on many twistor spaces, and it holds on Moishezon manifolds. Moreover, it is proved that a SKT manifold of dimension three on which the balanced cone equals the Gauduchon cone is in fact Kahler.
math.CV↗
The Kähler rank of compact complex manifolds
The Kähler rank was introduced by Harvey and Lawson in their 1983 paper as a measure of the {\it kählerianity} of a compact complex surface. In this work we generalize this notion to the case of compact complex manifolds and we prove several results related to this notion. We show that on class $VII$ surfaces, there is a correspondence between the closed positive forms on a surface and those on a blow-up in a point. We also show that a manifold of maximal Kähler rank which satisfies an additional condition is in fact Kähler.
math.CV↗
On compact complex surfaces of Kähler rank one
The Kähler rank of compact complex surfaces was introduced by Harvey and Lawson in their 1983 paper on Kähler manifolds as a measure of ``kälerianity''. Here we give a partial classification of compact complex surfaces of Kähler rank 1. These are either elliptic surfaces, or Hopf surfaces, or they admit a holomorphic foliation of a very special type. As a consequence we give an affirmative answer to the question raised by Harvey and Lawson whether the Kähler rank is a birational invariant.
math.CV↗