General Relativity: An Introduction for Physicists · Problem 7.9

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

Physics · curvature-tensor-two-dimensions

Problem

Show that in a two-dimensional Riemannian manifold all the components of

R_{abcd}

are equal either to zero or to

\pm R_{1212}