K\"ahler Immersions of ALE K\"ahler Manifolds into Complex Space Forms

Farnaz Ghanbari; Abbas Heydari

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arXiv · 2408.15551

K\"ahler Immersions of ALE K\"ahler Manifolds into Complex Space Forms

Farnaz Ghanbari·Abbas Heydari

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Abstract

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

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BibTeX RIS

Farnaz Ghanbari, Abbas Heydari. 2024-08-28. K\"ahler Immersions of ALE K\"ahler Manifolds into Complex Space Forms. https://arxiv.org/abs/2408.15551

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