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|
Curvature form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Curvature_form&oldid=16422