Curvature form
From Encyclopedia of Mathematics
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
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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
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and defines the holonomy algebra (see Holonomy group).
Comments
The equation is called the structure equation.
References
[a1] | S. Kobayashi, K. Nomizu, "Foundations of differential geometry" , 1 , Interscience (1963) pp. Chapt. V, VI |
How to Cite This Entry:
Curvature form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Curvature_form&oldid=32609
Curvature form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Curvature_form&oldid=32609
This article was adapted from an original article by Ü. Lumiste (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article