Namespaces
Variants
Actions

Curvature form

From Encyclopedia of Mathematics
Revision as of 18:17, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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://www.encyclopediaofmath.org/index.php?title=Curvature_form&oldid=16422
This article was adapted from an original article by Ü. Lumiste (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article