Difference between revisions of "Sphere bundle"

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(New page: ==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 ov...)
 
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Latest revision as of 12:35, 22 May 2008

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.