ansatz is [math]g_{mn}dy^mdy^n+W^2(y)g_{uv}(x)dx^udx^v[/math]

 

if [math]R_{uv}=\tilde{R}_{uv}-\frac{g_{uv}}{(p+1)W^{p-1}}\nabla^2W^{p+1}[/math] eq1

 

why eq 1 is???

 

[math]\frac{1}{p+1}(\tilde{R}W^{-2}-R)=pW^{-2}\nabla W \nabla W+W^{-1}\nabla^2W[/math]

 

i tried to multiplicate eq1 by [math]W^{-2}g^{uv}[/math] but i don't go to the result

It will get to the result, alejandrito. Where is the difficulty? Is it the right hand side?

It will get to the result, alejandrito. Where is the difficulty? Is it the right hand side?

 

to multiplicate by [math]W^{-2} g^{uv}[/math]

 

[math]R-W^{-2}\tilde{R}=-\frac{\nabla^2 (W^{p+1})}{W^{p+1}}[/math]

 

[math]\nabla^2(W^{p+1})=P(P+1)W^{P-1}\nabla W \nabla W+(P+1) W^P \nabla ^2 W[/math]

 

Ok......Sorry

 

I tried very time.......gap in my mind..........i'm crazy.........