Moving frame

Extrinsic moving frame

On a homogeneous space XG/H, a moving frame is a section of the tautological bundle GG/H. In every xX it provides a G-description of X "centered" at x (see homogeneous space#Intuitive approach). If we want to study a submanifold M of X it could be useful a section of the pullback bundle i(G), where i:MX is the inclusion map. This section is also called a moving frame on M.

Intrinsic moving frame

In the more general sense, it is a local section of a principal bundle: see principal bundle#Components of a section.

They are used in the method of moving frames.