• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.929-933
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• 2018

In this paper we show that complete noncompact harmonic Finsler manifolds with minimal horospheres are flat.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.365-374
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• 1995

On a compact manifold without conjugate points, the volume entropy can be obtained as the average mean curvature of the horospheres in the universal covering space. In the case when the volume entropy is zero, we prove that the universal covering space is diffeomorphic to a product space with a line factor. This fact can be considered as a surporting evidence for the Mane's conjecture, which claims the flatness of the mainfold.