# Cocurvature

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.

## Definition

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 T*M* such that *P _{a}^{b}P_{b}^{c}* =

*P*, then the cocurvature is a vector-valued 2-form on

_{a}^{c}*M*defined by

where *X* and *Y* are vector fields on *M*.

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