Sphere bundle

Definition

Loose bundle

The sphere bundle of a Riemannian manifold is defined as a (fiber) subbundle of the tangent bundle to the manifold, such that the fiber over a point is the set of all tangent vectors of length 1, at that point.

As a fiber bundle, the sphere bundle does not depend on the choice of Riemannian metric, and hence can be defined for any differential manifold.