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20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy: Difference between revisions
20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy (edit)
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But it was Atiyah who actually named the operator, and utilized its geometric significance. On a curved manifold it does not square to the Laplacian, but differs by the scalar curvature: | But it was Atiyah who actually named the operator, and utilized its geometric significance. On a curved manifold it does not square to the Laplacian, but differs by the scalar curvature: | ||
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<math> D^2s(x)=\Delta s(x)+\frac{1}{4} | <math> D^2s(x)=\Delta s(x)+\frac{1}{4}R s(x) </math> This is known as the Lichnerowicz formula. | ||
== Notes == | == Notes == | ||