Calculating Rii in Space with d-dimensions

[Physicor]

Hello my friends

I have a question about riemannian tensor. how Get Rii in space with d-dimentions? for example in coordinate taht linear element is
ds^2=(dx^2+dy^2+dz^2)/[1+/(K/4)*(x^2+y^2+z^2)] where K is Gaussian tensor.

Thanks!

 

[robphy]

do you mean "curvature" for K?

In any case, as it stands, this isn't really a relativity question... it's more of a tensor or differential geometry question...but it really sounds like a mathematics homework problem. What is your starting point? Show some work first.

 

[Chris Hillman]

Hi, Physicor,

I second what Rob said and add (if this is homework, I probably shouldn't) that you appear to have written down what might be the desired answer to a problem asking you to compute curvature of spatial hyperslices (orthogonal to the world lines of the matter) in an FRW model.

 

[Physicor]

But general Relativity depends this case. because when you talk about relativity, it is important that understanding some problems and subjects such as riemannian geometry & etc, specially for describtion of this answer that riemann proved it. there is a space with above line - element that K is gaussian curvature tensor (http://mathworld.wolfram.com/GaussianCurvature.html)

I can not understand this question " do you mean "curvature" for K? "

-------

thank u Chris Hillman. but my question didn't depend your answer.

____________

Good luck!