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Hermitian–Einstein metrics and jumping lines for Sp(n+1)-homogeneous bundles over ℙ2n+1

Published online by Cambridge University Press:  24 October 2008

Al Vitter
Al Vitter
Affiliation:
Mathematics Department, Tulane University, New Orleans, LA 70118, USA
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Extract

Stable holomorphic vector bundles over complex projective space ℙn have been studied from both the differential-geometric and the algebraic-geometric points of view.

On the differential-geometric side, the stability of E -→ ℙn can be characterized by the existence of a unique hermitian–Einstein metric on E, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn (see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙn and the nullcorrelation bundle (see [9] and [10]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 443 - 451
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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