The natural metric in the Horrocks-Mumford bundle is not Hermitian-Einstein

Details The natural metric in the Horrocks-Mumford bundle is not Hermitian-Einstein The natural metric in the Horrocks-Mumford bundle is not Hermitian-Einstein

2000-09-26

arxiv.org/abs/math/0009226v1

Mathematics

Differential Geometry

7 pages, LaTeX2e

Scientific paper

The Horrocks-Mumford bundle $E$ is a famous stable complex vector bundle of rank 2 on 4-dimensional complex projective space. By construction, $E$ has a natural Hermitian metric $h_1$. On the other hand, stability implies the existence of a Hermitian-Einstein metric in $E$ which is unique up to a positive scalar. Now the obvious question is if $h_1$ is in fact the Hermitian-Einstein metric. In this note we indicate how to show by computation that this is not the case.

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