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Lichnerowicz conjectured that all harmonic manifolds are symmetric spaces. It was proved that the conjecture fails for the noncompact manifolds. What is a harmonic manifold? I could not find it in wikipedia.

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1 
 What about MathSciNet? – Yemon Choi Jan 17 2012 at 6:21
Or Zentralblatt? – Yemon Choi Jan 17 2012 at 6:22
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 A Google search gives arxiv.org/abs/1007.0477 as the second hit. You did not try very hard, did you? – Angelo Jan 17 2012 at 6:45
Thanks Prof(s) and sorry that I bothered. Honestly, I tried, which might not be ``hard'' enough. I wanted a very simple description and I got it now, from the paper Y. Nikolayevsky (2005) Two theorems on harmonic manifolds. Downloaded arxiv.org/abs/1007.0477 also. – spr Jan 17 2012 at 11:45
Before closing: here's a nice reference: math.unice.fr/~frou/recherche/Damek-Ricci.pdf – Alain Valette Jan 17 2012 at 15:13

closed as off topic by Ryan Budney, Deane Yang, Alain Valette, Angelo, Gjergji Zaimi Jan 17 2012 at 20:19

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