A detailed look at the Calabi-Eguchi-Hanson spaces
arXiv:2201.07295 · doi:10.1007/s00022-025-00763-8
Abstract
This article takes a detailed look at the Ricci-flat metrics introduced by Eguchi-Hanson and Calabi on the canonical line bundle of complex projective space. We give a description of these spaces as resolutions of certain orbifold singularities. We then compute the curvature explicitly and show that all compact, minimal submanifolds are contained in the zero section. This extends a result by Tsai and Wang.
22 pages. The second version includes the following changes: Added a short result about the holomorphic volume form (Prop. 8), amended an important gap in the proof of Thm. 9, added a description of local coordinates on the canonical line bundle and described the metric in these coordinates (Eq. 22)