Moving frame

Extrinsic moving frame

On a homogeneous space $X\approx G/H$, a moving frame is a section of the tautological bundle $G\to G/H$. In every $x\in X$ 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 $i^{\ast }(G)$, where $i:M\to X$ 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. See also: invariant.