General Relativity: An Introduction for Physicists · Problem 7.11

The equivalence principle and spacetime curvature — Hobson, Efstathiou & Lasenby

Physics · gaussian-curvature-two-dimensions

Problem

For a two-dimensional manifold with line element

ds^2 = dr^2 + f^2(r)\,d\theta^2

, show that the Gaussian curvature is given by

K = -f''/f

, where a prime denotes

d/dr