Supriya Ghosh (Editor)

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 R ¯ P is a vector-valued 2-form on M defined by

R ¯ P ( X , Y ) = ( Id − P ) [ P X , P Y ]

where X and Y are vector fields on M.

References

Cocurvature Wikipedia
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