Alexander Pigazzini
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Example of steady Ricci soliton whith indefinite or nonpositive Ricci curvature
Accepted answer
5 votes

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^{-...

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Constant curvature difference surfaces
4 votes

..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 ...

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generalisation of umbilic surfaces
4 votes

..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 ...

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Einstein warped-product manifold with flat fiber
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3 votes

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)...

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From Riemannian curvature to Ricci curvature in warped product manifold
1 votes

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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Curvature of singular Riemannian metric
1 votes

When you lose the regularity , the situation has to be evaluated case by case , I don't think there are " general procedures " to operate ...

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