Editing Connection (principal bundle) (section)

===Pull back via trivializing section===
A trivializing section of a principal bundle ''<math>P</math>'' is given by a section ''s'' of ''<math>P</math>'' over an open subset ''<math>U</math>'' of ''<math>M</math>''. Then the [[pullback (differential geometry)|pullback]] ''s''<sup>*</sup>''ω'' of a principal connection is a 1-form on ''<math>U</math>'' with values in <math>\mathfrak g</math>.
If the section ''s'' is replaced by a new section ''sg'', defined by (''sg'')(''x'') = ''s''(''x'')''g''(''x''), where ''g'':''M''→''G'' is a smooth map, then <math>(sg)^* \omega = \operatorname{Ad}(g)^{-1}s^* \omega + g^{-1} dg</math>. The principal connection is uniquely determined by this family of <math>\mathfrak g</math>-valued 1-forms, and these 1-forms are also called '''connection forms''' or '''connection 1-forms''', particularly in older or more physics-oriented literature.