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 the differential of the ...

### Famous quotes containing the words bundle and/or frame:

“We styled ourselves the Knights of the Umbrella and the *Bundle*; for, wherever we went ... the umbrella and the *bundle* went with us; for we wished to be ready to digress at any moment. We made it our home nowhere in particular, but everywhere where our umbrella and *bundle* were.”

—Henry David Thoreau (1817–1862)

“A cold and searching wind drives away all contagion, and nothing can withstand it but what has a virtue in it, and accordingly, whatever we meet with in cold and bleak places, as the tops of mountains, we respect for a sort of sturdy innocence, a Puritan toughness. All things beside seem to be called in for shelter, and what stays out must be part of the original *frame* of the universe, and of such valor as God himself.”

—Henry David Thoreau (1817–1862)