Uniqueness of balanced metrics on holomorphic vector bundles

作者：Loi Andrea^*; Mossa Roberto

来源：Journal of Geometry and Physics, 2011, 61(1): 312-316.

DOI：10.1016/j.geomphys.2010.10.005

• Kahler metrics
• Balanced metric
• Balanced basis
• Holomorphic maps into Grassmannians
• Moment maps

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.

• 出版日期2011-1