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amazingopen45

  • 3 years ago

What is the ricci curvature in simple terms?

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  1. JamesJ
    • 3 years ago
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    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.

  2. amazingopen45
    • 3 years ago
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    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?

  3. JamesJ
    • 3 years ago
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    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.

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