Twistor quotients of hyperkaehler manifolds
Differential Geometry
2007-05-23 v1
Abstract
We generalize the hyperkaehler quotient construction to the situation where there is no group action preserving the hyperkaehler structure but for each complex structure there is an action of a complex group preserving the corresponding complex symplectic structure. Many (known and new) hyperkaehler manifolds arise as quotients in this setting. For example, all hyperkaehler structures on semisimple coadjoint orbits of a complex semisimple Lie group arise as such quotients of . The generalized Legendre transform construction of Lindstroem and Rocek is also explained in this framework.
Cite
@article{arxiv.math/0006142,
title = {Twistor quotients of hyperkaehler manifolds},
author = {Roger Bielawski},
journal= {arXiv preprint arXiv:math/0006142},
year = {2007}
}