# Is there a harmonic function on $M = R \times {}_{{e^{2t}}}N$

M is a warped product $M = R \times {}_{{e^{2t}}}N$.N is the spherical suspension over$R{P^2}$.N is an Alexandrov space but not a manifold.So is M.Is there a harmonic function on M?What if we replace ${e^{2t}}$ by ${\cosh ^2}\left( t \right)$?

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