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_a^bP_b^c = P_a^c, then the cocurvature ${\displaystyle {\bar {R}}_{P}}$  is a vector-valued 2-form on M defined by

${\displaystyle {\bar {R}}_{P}(X,Y)=(\operatorname {Id} -P)[PX,PY]}$ 

where X and Y are vector fields on M.

• Curvature
• Lie bracket
• Frölicher-Nijenhuis bracket

• Kolář, Ivan; Michor, Peter W.; Slovák, Jan (1993). Natural operations in differential geometry. Berlin: Springer-Verlag. ISBN 3-540-56235-4. MR 1202431. Zbl 0782.53013.