Busemann Functions in a Harmonic Manifold

For a noncompact complete and simply connected harmonic manifold M, we prove the analyticity of Busemann functionson M. This is the main result of this paper. An application of it shows that the harmonic spaces having minimal horospheres have the bi-asymptotic property. Finally, we prove that the total Busemann functionis continuous in Ctopology. As a consequence, we show that the uniform divergence of geodesics holds in these spaces.