A detailed look at the Calabi-Eguchi-Hanson spaces

TL;DR

This paper provides a detailed analysis of Ricci-flat Calabi-Eguchi-Hanson spaces, describing their structure as resolutions of orbifold singularities, computing their curvature explicitly, and examining their minimal submanifolds.

Contribution

It offers a comprehensive description of Calabi-Eguchi-Hanson spaces, including explicit curvature calculations and an extension of known results on minimal submanifolds.

Findings

Spaces are resolutions of orbifold singularities

Curvature is explicitly computed

All compact minimal submanifolds lie in the zero section

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.