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arXiv · 2309.02226

Asymptotically harmonic manifolds of dimension 3 with minimal horospheres

Jihun Kim·JeongHyeong Park·Hemangi Madhusudan Shah
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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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Jihun Kim, JeongHyeong Park, Hemangi Madhusudan Shah. 2023-09-05. Asymptotically harmonic manifolds of dimension 3 with minimal horospheres. https://arxiv.org/abs/2309.02226

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