1996/04/30 by Ioannis Bakas, I. Bakas, K. Sfetsos +1 · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry and complex manifolds #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.1142/s0217751x97001456
published as Int.J.Mod.Phys. A12 (1997) 2585-2612 · A few typos have been corrected; final version
openalex publication_date 1997/06/10 · arxiv created 1997/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Eguchi–Hanson, Taub–NUT and Atiyah–Hitchin metrics are the only complete nonsingular SO(3)-invariant hyper-Kahler metrics in four dimensions. The presence of a rotational SO(2) isometry allows their unified treatment based on solutions of the 3D continual Toda equation. We determine the Toda potential in each case and examine the free field realization of the corresponding solutions, using infinite power series expansions. The Atiyah–Hitchin metric exhibits some unusual features attributed to topological properties of the group of area preserving diffeomorphisms. The construction of a descending series of SO(2)-invariant 4D regular hyper-Kahler metrics remains an interesting question.