The natural metric in the Horrocks-Mumford bundle is not Hermitian-Einstein
O. F. B. van Koert, M. Lubke
Abstract
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 h1. 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 h1 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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