HyperKähler Potentials in Cohomogeneity Two
Abstract
A hyperKähler potential is a function rho that is a Kähler potential for each complex structure compatible with the hyperKähler structure. Nilpotent orbits in a complex simple Lie algebra are known to carry hyperKähler metrics admitting such potentials. In this paper, we explicitly calculate the hyperKähler potential when the orbit is of cohomogeneity two. In some cases, we find that this structure lies in a oneparameter family of hyperKähler metrics with Kähler potentials, generalising the EguchiHanson metrics in dimension four.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2000
 arXiv:
 arXiv:math/0001024
 Bibcode:
 2000math......1024K
 Keywords:

 Differential Geometry;
 53C25 (Primary) 17B45;
 57S25 (Secondary)
 EPrint:
 21 pages, LaTeX with AMS macros