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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]
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Abstract

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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

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3. Kobayashi, S., Homogenous vector bundles and stability, Nagoya Math. J. 101( 1986), 37–54.Google Scholar