Uniqueness of balanced metrics on holomorphic vector bundles

Abstract

Let $E\to M$ be a holomorphic vector bundle over a compact Kaehler manifold $(M,\omega )$. We prove that if $E$ admits a $\omega$-balanced metric (in X. Wang's terminology) then it is unique. This result together with a result of L. Biliotti and A. Ghigi 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 Kaehler maps into Grassmannians.

arXiv comment7 pages

References in corpus (1)

• Numerical Algorithms for Finding Balanced Metrics on Vector Bundles

Cited by in corpus (4)

• Some remarks on homogeneous Kähler manifolds
• A note on diastatic entropy and balanced metrics
• Approximation of Regular Sasakian Manifolds
• Balanced metrics on homogeneous vector bundles