Can anyone explain the concept of manifold and Reimanni manifold in plain language ?? And what are its applications??
How so? The riemannian metric allows you to calculate the arc lengths of differentiable curves; this is not the same thing that a metric equipped to a metric space does. What notion of distance are you alluding to?The Riemann metric gives the family of inner products at a point, and in turn gives you the notion of distance on the manifold.