Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T15:35:24.425Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle

Published online by Cambridge University Press:  20 November 2018

Piotr M. Zelewski
Piotr M. Zelewski*
Affiliation:
McMaster University, Department of Mathematics and Statistics, Hamilton, Ontario, L8P3N8, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that any holomorphic, homogenous vector bundle admits a homogenous minimal metric—a metric for which the Hermitian-Einstein tensor is diagonal in a suitable sense. The concept of minimality depends on the choice of the Jordan-Holder filtration of the corresponding parabolic module. We show that the set of all admissible Hermitian-Einstein tensors of certain class of minimal metrics is a convex subset of the euclidean space. As an application, we obtain an algebraic criterion for semistability of homogenous holomorphic vector bundles.

Keywords

53C3014M15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 3 , 01 June 1993 , pp. 662 - 672
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Donaldson, S., Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50(1985), 1–26.Google Scholar
2. Uhlenbeck, K. and Yau, S. T., On the Existence of Hermitian-Yang-Mills Connections in Stable Vector Bundles, Comm. Pure and Applied Math. XXXIX(1986), S257–S293.Google Scholar
3. Kobayashi, S., Homogenous vector bundles and stability, Nagoya Math. J. 101( 1986), 37–54.Google Scholar