Corpus ID: 119132625

Numerically flat holomorphic bundles over non K\"ahler manifolds

@article{Li2019NumericallyFH,
title={Numerically flat holomorphic bundles over non K\"ahler manifolds},
author={Chao Li and Ya Nie and Xi Cheng Zhang},
journal={arXiv: Differential Geometry},
year={2019}
}
• Published 15 January 2019
• Mathematics
• arXiv: Differential Geometry
In this paper, we study numerically flat holomorphic vector bundles over a compact non-K\"ahler manifold $(X, \omega)$ with the Hermitian metric $\omega$ satisfying the Gauduchon and Astheno-K\"ahler conditions. We prove that numerically flatness is equivalent to numerically effectiveness with vanishing first Chern number, semistablity with vanishing first and second Chern numbers, approximate Hermitian flatness and the existence of a filtration whose quotients are Hermitian flat. This gives an…
1 Citations

References

SHOWING 1-10 OF 25 REFERENCES
Existence of approximate Hermitian-Einstein structures on semi-stable bundles
The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is
A note on semistable Higgs bundles over compact Kähler manifolds
• Mathematics
• 2015
In this note, by using the Yang–Mills–Higgs flow, we show that semistable Higgs bundles with vanishing first and second Chern numbers over compact Käher manifolds must admit a filtration whose
HARDER–NARASIMHAN FILTRATION ON NON KÄHLER MANIFOLDS
In this paper we are interested in the behavior of the degree map on holomorphic bundles over compact complex manifolds. We do not assume the manifold to be Kahler and we define the degree by means
Holomorphic tensors and vector bundles on projective varieties
In this paper we study vector bundles on varieties of dimension greater than one. To do this, we apply the theory of equivariant model maps developed in the paper. We prove a topological criterion
A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds
• Mathematics
Épijournal de Géométrie Algébrique
• 2018
A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the
A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry
• Mathematics
• 1993
It is the purpose of this paper to introduce and study a nonlinear elliptic system of equations imposed on a map from a Hermitian into a Riemannian manifold which seems to be more appropriate to
Semistable Higgs Bundles Over Compact Gauduchon Manifolds
• Mathematics
• 2016
In this paper, we consider the existence of approximate Hermitian–Einstein structure and the semi-stability on Higgs bundles over compact Gauduchon manifolds. Using the continuity method, we show
On projectively flat Hermitian manifolds
• Mathematics
• 1994
Let (M,g) be a n-dimensional compact hermitian manifold, with n > 2. (M, g) will be called projectively flat, if its curvature matrix is of the form 0 = a/n, where a is a (1, l)-form. Note that any
Astheno-K\"ahler and balanced structures on fibrations
• Mathematics
• 2016
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-Kahler metrics. We prove that the
On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics
• Mathematics
• 2017
Abstract In this note, we construct, for every n ≥ 4 , a non-Kahler compact complex manifold X of complex dimension n admitting a balanced metric and an astheno-Kahler metric, which is in addition k