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
 |
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).
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