scalar curvature in a sentence

Examples

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