# Palatini identity

In general relativity and tensor calculus, the Palatini identity is:

${\displaystyle \delta R_{\mu \nu }{}=(\delta \Gamma ^{\lambda }{}_{\mu \lambda })_{;\nu }-(\delta \Gamma ^{\lambda }{}_{\mu \nu })_{;\lambda }}$

where ${\displaystyle \delta \Gamma ^{\lambda }{}_{\mu \nu }}$ denotes the variation of Christoffel symbols[1] and semicolon ";" indicates covariant differentiation.

Proof can be found in the entry Einstein–Hilbert action.