Bernhard Riemann | Riemann zeta function | Riemann surface | Riemann hypothesis | Electromagnetic tensor | Riemann sphere | Riemann solver | Riemann-Roch theorem | Hugo Riemann | Einstein tensor | Riemann Xi function | Riemann's function | Riemann's existence theorem | Riemann–Roch theorem | Riemann manifold | Riemann integral | Riemann | Generalized Riemann Hypothesis | Fritz Riemann | Codazzi tensor |
Variation of the first term of the action with respect to the tetrad gives the (mixed index) Einstein tensor and variation of the second term with respect to the tetrad gives a quantity that vanishes by symmetries of the Riemann tensor (specifically the first Bianchi identity), together these imply Einstein's vacuum field equations hold.
In 1957, at a conference at Chapel Hill, North Carolina, appealing to various mathematical tools developed by John Lighton Synge, A. Z. Petrov and André Lichnerowicz, Pirani explained more clearly than had previously been possible the central role played by the Riemann tensor and in particular the tidal tensor in general relativity.