https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Ricci_curvature_determines_Ricci_curvature_tensorRicci curvature determines Ricci curvature tensor - Revision history2026-10-27T02:23:47ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Ricci_curvature_determines_Ricci_curvature_tensor&diff=1938&oldid=prevVipul: New page: ==Statement== ===Verbal statement=== The Ricci curvature of a Riemannian manifold (i.e., the value of Ricci curvature tensor for unit tangent vectors) determines the [[Ricci curv...2008-05-22T12:54:44Z<p>New page: ==Statement== ===Verbal statement=== The <a href="/wiki/Ricci_curvature" title="Ricci curvature">Ricci curvature</a> of a <a href="/wiki/Riemannian_manifold" title="Riemannian manifold">Riemannian manifold</a> (i.e., the value of Ricci curvature tensor for unit tangent vectors) determines the [[Ricci curv...</p>
<p><b>New page</b></p><div>==Statement==<br />
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===Verbal statement===<br />
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The [[Ricci curvature]] of a [[Riemannian manifold]] (i.e., the value of Ricci curvature tensor for unit tangent vectors) determines the [[Ricci curvature tensor]] of the manifold.<br />
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==Facts used==<br />
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* [[Ricci curvature tensor is symmetric]]<br />
* [[Symmetric bilinear form is determined by values on same-vector pairs]]<br />
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==Proof==<br />
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{{fillin}}</div>Vipul