Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 38B / c / Solution

Using the stated convention for the Riemann curvature tensor, the first independent component isThe other isusing the hyperbolic Pythagorean identity ${\coth }^{2}r-{\mathrm{csch}}^{2}r=1$. Antisymmetry in the final two indices supplies the components with those indices reversed. These are the curvature of the two-dimensional hyperbolic polar metric components.