The balanced metrics and cscK metrics on certain holomorphic ball bundles

2022 ◽  
pp. 104452
Author(s):  
Zhiming Feng ◽  
Zhenhan Tu
Keyword(s):  
Balanced Metrics

scholarly journals A parabolic flow of balanced metrics

2017 ◽  
Vol 2017 (723) ◽  
Author(s):  
Lucio Bedulli ◽  
Luigi Vezzoni
Keyword(s):  
Vector Bundle ◽  
Evolution Equation ◽  
Existence And Uniqueness ◽  
General Criterion ◽  
Balanced Metrics ◽  
Time Solution ◽  
Parabolic Flow ◽  
Short Time

AbstractWe prove a general criterion to establish existence and uniqueness of a short-time solution to an evolution equation involving “closed” sections of a vector bundle, generalizing a method used by Bryant and Xu [

scholarly journals Radial balanced metrics on the unit ball of the Kepler manifold

2019 ◽  
Vol 475 (1) ◽  
pp. 736-754 ◽  
Author(s):  
Hélène Bommier-Hato ◽  
Miroslav Engliš ◽  
El-Hassan Youssfi
Keyword(s):  
Unit Ball ◽  
Balanced Metrics

scholarly journals A flow of conformally balanced metrics with Kähler fixed points

2019 ◽  
Vol 374 (3-4) ◽  
pp. 2005-2040 ◽  
Author(s):  
Duong H. Phong ◽  
Sebastien Picard ◽  
Xiangwen Zhang
Keyword(s):  
Fixed Points ◽  
Balanced Metrics

BERGMAN AND BALANCED METRICS ON COMPLEX MANIFOLDS

2005 ◽  
Vol 02 (04) ◽  
pp. 553-561 ◽  
Author(s):  
ANDREA LOI
Keyword(s):  
Complex Manifold ◽  
Sufficient Conditions ◽  
Einstein Metric ◽  
Complex Manifolds ◽  
Balanced Metrics ◽  
Bochner’S Coordinates

In this paper we find sufficient conditions for a Bergman Einstein metric on a complex manifold to be balanced in terms of its Bochner's coordinates.

scholarly journals BALANCED METRICS ON HOMOGENEOUS VECTOR BUNDLES

2011 ◽  
Vol 08 (07) ◽  
pp. 1433-1438 ◽  
Author(s):  
ROBERTO MOSSA
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Holomorphic Vector Bundle ◽  
Kähler Manifold ◽  
Balanced Metrics ◽  
Kahler Manifold ◽  
Balanced Metric ◽  
Compact Kähler Manifold ◽  
Homogeneous Variety ◽  
Homogeneous Vector

Let E → M be a holomorphic vector bundle over a compact Kähler manifold (M, ω) and let E = E1 ⊕ ⋯ ⊕ Em → M be its decomposition into irreducible factors. Suppose that each Ej admits a ω-balanced metric in Donaldson–Wang terminology. In this paper we prove that E admits a unique ω-balanced metric if and only if [Formula: see text] for all j, k = 1,…, m, where rj denotes the rank of Ej and Nj = dim H0(M, Ej). We apply our result to the case of homogeneous vector bundles over a rational homogeneous variety (M, ω) and we show the existence and rigidity of balanced Kähler embedding from (M, ω) into Grassmannians.

scholarly journals Balanced metrics on Cn

2007 ◽  
Vol 57 (4) ◽  
pp. 1115-1123 ◽  
Author(s):  
Fabrizio Cuccu ◽  
Andrea Loi
Keyword(s):  
Balanced Metrics

scholarly journals A note on diastatic entropy and balanced metrics

2014 ◽  
Vol 86 ◽  
pp. 492-496 ◽  
Author(s):  
Roberto Mossa
Keyword(s):  
Balanced Metrics

scholarly journals Balanced metrics on Cartan and Cartan–Hartogs domains

2011 ◽  
Vol 270 (3-4) ◽  
pp. 1077-1087 ◽  
Author(s):  
Andrea Loi ◽  
Michela Zedda
Keyword(s):  
Balanced Metrics ◽  
Hartogs Domains

scholarly journals Balanced metrics on non-Kähler Calabi-Yau threefolds

2012 ◽  
Vol 90 (1) ◽  
pp. 81-129 ◽  
Author(s):  
Jixiang Fu ◽  
Jun Li ◽  
Shing-Tung Yau
Keyword(s):  
Balanced Metrics

scholarly journals Astheno–Kähler and Balanced Structures on Fibrations

2017 ◽  
Vol 2019 (22) ◽  
pp. 7093-7117 ◽  
Author(s):  
Anna Fino ◽  
Gueo Grantcharov ◽  
Luigi Vezzoni
Keyword(s):  
Homogeneous Spaces ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kähler Metrics ◽  
Hermitian Metrics ◽  
Kahler Metrics ◽  
Balanced Metrics ◽  
Invariant Volume ◽  
Balanced Metric ◽  
First Chern Class

Abstract We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, strong Kähler with torsion (SKT), and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then we provide a construction of astheno-Kähler structures on torus bundles over Kähler manifolds leading to new examples. In particular, we find examples of compact complex non-Kähler manifolds which admit a balanced and an astheno-Kähler metric, thus answering to a question in [52] (see also [24]). One of these examples is simply connected. We also show that the Lie groups SU(3) and G2 admit SKT and astheno-Kähler metrics, which are different. Furthermore, we investigate the existence of balanced metrics on compact complex homogeneous spaces with an invariant volume form, showing in particular that if a compact complex homogeneous space M with invariant volume admits a balanced metric, then its first Chern class c1(M) does not vanish. Finally we characterize Wang C-spaces admitting SKT metrics.

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