Some Examples of Projective and c-projective Compactifications of Einstein Metrics

We construct several examples of compactifications of Einstein metrics. We show that the Eguchi–Hanson instanton admits a projective compactification which is non-metric, and that a metric cone over any (pseudo)-Riemannian manifolds admits a metric projective compactification. We construct a para- c -projective compactification of neutral signature Einstein metrics canonically defined on certain rank- n affine bundles M over n -dimensional manifolds endowed with projective structures.