English

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

Differential Geometry 2024-08-29 v1

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.

Keywords

Cite

@article{arxiv.2408.15551,
  title  = {K\"ahler Immersions of ALE K\"ahler Manifolds into Complex Space Forms},
  author = {Farnaz Ghanbari and Abbas Heydari},
  journal= {arXiv preprint arXiv:2408.15551},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with arXiv:1712.04298 by other authors