I was browsing wikipedia and was puzzeling about what is the difference between:
For 2-dimensional surfaces they both describe the "Gaussian curvature" https://en.wikipedia.org/wiki/Gaussian_curvature
(From the scalar curvature page "the scalar curvature is twice the Gaussian curvature")
So that made me wonder, they both seem to describe the same thing (curvature of a manifold ) but how are they related, and how can you calculate one from the other?
Also I was editing the page on hyperbolic geometry on wikipedia https://en.wikipedia.org/wiki/Hyperbolic_geometry and was wondering to which of the three curvatures I should refer.
For the two dimensional case I can safely refer to the Gaussian curvature , but for higher dinensional cases which curvature is correct/best?
PS Under similar question I found Relationship beween Ricci curvature and sectional curvature, but am not sure if that makes this question a duplicate (if anything that question is about positive curvature, while mine is about negative curvature)