integrais DE ANCELMO L. GRACELI. Ricci curvature tensor It is a standard exercise of (multi)linear algebra to verify that this definition does not depend on the choice of the basis � 1 , … , � � . In abstract index notation , R i c � � = R � � � � = R � � � � . Sign conventions. Note that some sources define � ( � , � ) � to be what would here be called − � ( � , � ) � ; they would then define Ric � as − tr ( � ↦ R � ( � , � ) � ) . Although sign conventions differ about the Riemann tensor, they do not differ about the Ricci tensor. INTEGRAIS DE ANCELMO L. GRACELI X [ ] = -S t [ ] dt ...