2000/01/05 by Piotr Kobak, Andrew Swann, Kobak, Piotr +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #53C25 (Primary) 17B45 #57S25 (Secondary) #Biological Activity of Diterpenoids and Biflavonoids #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.DG #msc:17B45 #msc:53C25 #msc:57S25
paper · pdf · doi:10.48550/arxiv.math/0001024
21 pages, LaTeX with AMS macros
arxiv created 2000/01/05 · openalex publication_date 2000/01/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 one-parameter family of hyperKähler metrics with Kähler potentials, generalising the Eguchi-Hanson metrics in dimension four.