Geodesic
On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle
Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 662-672

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1993-037-5
Mots-clés : 53C30, 14M15 
Zelewski, Piotr M. On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle. Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 662-672. doi: 10.4153/CJM-1993-037-5
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