English

Asymptotically harmonic manifolds of dimension 3 with minimal horospheres

Differential Geometry 2023-09-06 v1

Abstract

In [14], it was shown that, if M is a 3-dimensional asymptotically harmonic with minimal horospheres, then M is flat. However, there is a gap in the proof of this paper. In this paper, we provide the correct proof of the result. Thus we complete the classification of asymptotically harmonic manifolds of dimension 3: An asymptotically harmonic manifold of dimension 3 is either a flat or real hyperbolic space.

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Cite

@article{arxiv.2309.02226,
  title  = {Asymptotically harmonic manifolds of dimension 3 with minimal horospheres},
  author = {Jihun Kim and JeongHyeong Park and Hemangi Madhusudan Shah},
  journal= {arXiv preprint arXiv:2309.02226},
  year   = {2023}
}

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7 pages