Question

What is the ricci curvature in simple terms?

Answer 1

Ricci curvature a slightly sophisticated concept and it's hard to know what simple might be here.

Mathematically, maybe one simple way to understand is as a function of the metric tensor, g, in a local coordinate system is

\[R_{ij} = (-3/2) \Delta g_{ij}\]
But even that can be obscure. The best thing to do at first to begin to get a sense of R_ij is is to work some examples for simple geometries: e.g., flat space, a sphere and a cylinder.

Answer 2

Thanks so much! But what is delta g_ij?
I only know that it is used in finding distance in 4-d where c^2=a^2+b^2 doesn't work. So the ds^2=g_ij*dx_i*dx_j=dt^2-dx^2-dy^2-dz^2.

Also what is the first, second, and third componets of momentum?

Answer 3

I recommend you go to the library and find a good textbook that works some examples; that is the best way to get a feel for this.

In the expression I wrote, g_ij is the metric tensor and the delta is the Laplacian operator.