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

Publication date: 26 September 2000

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

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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