# Cocurvature

If M is a manifold and P is a connection on M, that is a vector-valued 1-form on M which is a projection on TM such that PabPbc = Pac, then the cocurvature ${\displaystyle {\bar {R}}_{P}}$ is a vector-valued 2-form on M defined by
${\displaystyle {\bar {R}}_{P}(X,Y)=(\operatorname {Id} -P)[PX,PY]}$