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I have found doing some calculation that the metric:
$$g(t)=\frac{dx^2+dy^2}{e^{-4t}-x^2-y^2}$$
satisfies $\frac{dg(t)}{dt}=-2Ric(t)$
Where
$$\frac{dg(t)}{dt}=\frac{4e^{-4t}(dx^2+dy^2)}{(e^{-...

..a small addition to Professor Bryant's answer
For this class of surfaces, where $k1-k2 = constant$, we have introduced the name "Costant Skew Curvature Surfaces" (CSkC-surfaces) and we have studied ...

..a small addition to Professor Bryant's answer
For this class of surfaces, where $k1-k2 = constant$, we have introduced the name "Costant Skew Curvature Surfaces" (CSkC-surfaces) and we have studied ...

When we have an Einstein warped-product manifold where the base is a Riemannian manifold, independently of dimension, and the ﬁber is a Ricci-ﬂat, we have: $|\nabla f|^2+[\frac{\lambda (m-n)+ R}{m(m-1)...

In Besse "Einstein Manifold" in Corollary 9.105 you can find:
Here, you can guess how (9.105c), (9.105e) and (9.105d) can contribute to (9.106a) which is yours (2).

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