Kähler Immersions of ALE Kähler Manifolds into Complex Space Forms

In this article, we investigate the Kähler immersions of special Asymptotically Locally Euclidean (ALE) Kähler metrics into complex space forms. We provide a relation between Kähler immersions problem of these metrics and the sign of their mass. Our result shows that these metrics with positive mass do not admit a Kähler immersion into complex Euclidean space. Moreover, we also obtain that these metrics with any sign of mass cannot be Kähler immersed into complex hyperbolic space.