The value of curl(curl A) - grad(div A) + div(grad A) for an absolute vector A

摘要

The well-known identity involving the expression presented in the above titleis considered in Riemannian and in Euclidean space without restriction on thecoordinate system adopted therein. The Riemann and Ricci tensors intrinsicallyassume a defining role in the analysis. The analysis is designed to put an endto the myriad of confusing and mostly incorrect statements about the identity,which are found in textbooks and in the literature.