The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.2010 Mathematics Subject Classification. 53C25, 53C35.
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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