What is the relation between two Riemannian metrics with the same Riemannian curvatures?

Asked Jun 05 '15 at 17:58

Active Jun 05 '15 at 17:58

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Consider two flat Riemannian metrics on a manifold. What is the general relation between these two metrics if the manifold is not simply-connected? What is the answer if two Riemannian metrics have the same non-flat Riemannian curvature?

Can anyone suggest me relevant references that deal with this problem?

Thanks, Arzhang

asked Jun 05 '15 at 17:58

Arzhang

3

Relevant :http://mathoverflow.net/questions/100281/does-the-curvature-determine-the-metric?rq=1 – Paul Reynolds Jun 05 '15 at 18:37

What is the relation between two Riemannian metrics with the same Riemannian curvatures?

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