scalar curvature on one - dimensional Riemannian Manifold

Question

How can i express the scalar curvature for a one - dimensional Riemannian manifold (M, g) in terms of the metric g ?

Answer 1

A one-dimensional Riemannian manifold does not have any intrinsic curvature at all. It is always locally isometric to a straight, "flat" line.

Formally, the Riemann curvature tensor has but a single component $R_{1111}$, but this element is required to be 0 due to (for example) the skew-symmetry of $R_{ijkl}$.