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

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dc.creatorvan Koert, O. F. B.
dc.creatorLubke, M.
dc.date2000-09-26
dc.date.accessioned2026-07-07T04:37:41Z
dc.date.available2026-07-07T04:37:41Z
dc.descriptionThe 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.
dc.description7 pages, LaTeX2e
dc.identifierhttps://arxiv.org/abs/math/0009226
dc.identifierhttp://arxiv.org/abs/math/0009226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59997
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.titleThe natural metric in the Horrocks-Mumford bundle is not Hermitian-Einstein
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