Some examples of projective and $c$--projective compactifications of Einstein metrics

Abstract

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.