Английская Википедия:Cocurvature
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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 TM such that PabPbc = Pac, then the cocurvature <math>\bar{R}_P</math> is a vector-valued 2-form on M defined by
- <math>\bar{R}_P(X,Y) = (\operatorname{Id} - P)[PX,PY]</math>
where X and Y are vector fields on M.
See also
References
Шаблон:Differential-geometry-stub
