| 11. | The Yamabe problem is the following : Given a smooth, conformal to for which the scalar curvature of is constant?
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| 12. | This operator often makes an appearance when studying how the scalar curvature behaves under a conformal change of a Riemannian metric.
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| 13. | Here R ( g ) is the scalar curvature constructed from the metric g _ { \ mu \ nu }.
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| 14. | Where Rm is the full Riemann curvature tensor, Rc is the Ricci curvature tensor, and R is the scalar curvature.
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| 15. | Thus every manifold of dimension at least 3 has a metric with negative scalar curvature, in fact of constant negative scalar curvature.
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| 16. | Thus every manifold of dimension at least 3 has a metric with negative scalar curvature, in fact of constant negative scalar curvature.
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| 17. | Diego L . Rapoport, on the other hand, associates the relativistic quantum potential with the metric scalar curvature ( Riemann curvature ).
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| 18. | Where ? is the Laplace-Beltrami operator ( of negative spectrum ), and " R " is the scalar curvature.
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| 19. | It is also exactly half the scalar curvature of the 2-manifold, while the Ricci curvature tensor of the surface is simply given by
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| 20. | Yau and Schoen continued their work on manifolds with positive scalar curvature, which led to Schoen's final solution of the Yamabe problem.
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