Normal bundle
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In differential geometry, a field of mathematics, a normal bundle is a particular kind of vector bundle.
[edit] Definition
Let (M,g) be a Riemannian manifold, and 
a Riemannian submanifold. Define, for a given 
, a vector 
to be normal to S whenever g(n,v) = 0 for all 
(so that n is orthogonal to TpS). The set NpS of all such n is then called the normal space to S at p.
Just as the total space of the tangent bundle to a manifold is constructed from all tangent spaces to the manifold, the total space of the normal bundle NS to S is defined as
.
The conormal bundle is defined as the dual bundle to the normal bundle. It can be realised naturally as a sub-bundle of the cotangent bundle.
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