Uniqueness of balanced metrics on holomorphic vector bundles

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Loi, Andrea¹  Mossa, Roberto¹ 

[1] Univ Cagliari, Dipartimento Matemat & Informat, I-09124 Cagliari, Italy

关键词: Kahler metrics;    Balanced metric;    Balanced basis;    Holomorphic maps into Grassmannians;    Moment maps;   

DOI  :  10.1016/j.geomphys.2010.10.005

来源: Elsevier

【 摘 要 】

Let E -> M be a holomorphic vector bundle over a compact Kahler manifold (M, omega). We prove that if E admits a omega-balanced metric (in X. Wang's terminology (Wang, 2005 [3])) then it is unique. This result together with Biliotti and Ghigi (2008) [14] implies the existence and uniqueness of omega-balanced metrics of certain direct sums of irreducible homogeneous vector bundles over rational homogeneous varieties. We finally apply our result to show the rigidity of omega-balanced Kahler maps into Grassmannians. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free