Twistor quotients of hyperkaehler manifolds

Details Twistor quotients of hyperkaehler manifolds Twistor quotients of hyperkaehler manifolds

2000-06-20

arxiv.org/abs/math/0006142v1

Mathematics

Differential Geometry

Scientific paper

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 $G$ arise as such quotients of $T^*G$. The generalized Legendre transform construction of Lindstroem and Rocek is also explained in this framework.

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