The **tangent frame bundle** (or simply the **frame bundle**) of a smooth manifold *M* is the frame bundle associated to the tangent bundle of *M*. The frame bundle of *M* is often denoted F*M* or GL(*M*) rather than F(*TM*). If *M* is *n*-dimensional then the tangent bundle has rank *n*, so the frame bundle of *M* is a principal GL_{n}(**R**) bundle over *M*.

Read more about this topic: Frame Bundle

### Other articles related to "tangent frame bundle, frame bundle, bundle, frame, tangent":

**Tangent Frame Bundle**- Solder Form

... The

**frame bundle**of a manifold M is a special type of principal

**bundle**in the sense that its geometry is fundamentally tied to the geometry of M ... Let x be a point of the manifold M and p a

**frame**at x, so that is a linear isomorphism of Rn with the

**tangent**space of M at x ... The solder form of FM is the Rn-valued 1-form θ defined by where ξ is a

**tangent**vector to FM at the point (x,p), p-1TxM → Rn is the inverse of the

**frame**map, and dπ is ...

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