In mathematics in the branch of differential geometry, the cocurvature of a connection on a manifold is the obstruction to the integrability of the vertical bundle.
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 P<sub>a</sub><sup>b</sup>P<sub>b</sub><sup>c</sup> = P<sub>a</sub><sup>c</sup>, then the cocurvature is a vector-valued 2-form on M defined by
where X and Y are vector fields on M.