Curvature form

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A -form on a principal fibre bundle with structure Lie group , taking values in the Lie algebra of the group and defined by the connection form on by the formula

The curvature form is a measure of the deviation of the given connection from the locally flat connection characterized by the condition . It satisfies the Bianchi identity

and defines the holonomy algebra (see Holonomy group).


The equation is called the structure equation.


[a1] S. Kobayashi, K. Nomizu, "Foundations of differential geometry" , 1 , Interscience (1963) pp. Chapt. V, VI
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Curvature form. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Ü. Lumiste (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article