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1answer
24 views
what is the inner product appeared in front of the integral?
Given a compact manifold with a Riemannian metric $g$, we define the total
scalar curvature by
$$E(g)=\int_M RdV$$
Let us consider the first variation of $E$ under an arbitrary change of metric. We ...
1
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0answers
54 views
Energy functional
During my study on Ricci Flow I faced some functional known as enery functional. For example Einstein-Hilbert functional is called an energy functional, also in Perelman's works ...
4
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1answer
76 views
Problem about Ricci Flow
On page 12 of "Lectures On Ricci Flow" by Peter Topping is written:
In two dimensions, we know that the Ricci curvature can be written in
terms of the Gauss curvature $K$ as $Ric(g) = Kg$. Working ...
