M is a hyperbolic cone over an n1 dim Riemannian manifold N with $Ric(N) \ge  \left( {n  2} \right)$ ie $M = R \times {}_{\cosh \left( t \right)}N$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.
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