A new proof of the theorem: Harmonic manifolds with minimal horospheres are flat |
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Authors: | HEMANGI M SHAH |
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Institution: | 1. Harish Chandra Research Institute, Chhatnag Road, Jhusi, 211 019, India
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Abstract: | In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem. We also confirm that if a harmonic manifold M has same volume density function as ? n , then M is flat. |
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