Keywords

• metric tensor
• cognet
• verifying the linear relationship between mass tensor and curvature

Reimmanian Manifold from metric space

Suppose that you ONLY know a Riemannian manifold as a metric space---that is you know the point set and the distance between any two points, but you do not know the metric tensor or even the differentiable structure. Can you nevertheless reconstruct these from the distance function. The answer is that you can. See here