Line bundles on spectral curves and the generalised Legendre transform construction of hyperkahler metrics

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Bielawski, Roger

关键词: Spectral curves;    Hyperkaehler metrics;    Integrable systems;    Magnetic monopoles;   

DOI  :  10.1016/j.geomphys.2008.11.010

来源: Elsevier

【 摘 要 】

An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K subset of GL(k) is one of the following: maximal parabolic, maximal torus, GL(k - 1) embedded diagonally. The generalised Legendre transform construction of hyperkahler metrics is studied further, showing that many known hyperkahler metrics (including the ones on coadjoint orbits) arise in this way. and giving a large class of new (pseudo-)hyperkahler metrics, analogous to monopole metrics. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free