In the mathematical field of differential geometry, a normal bundle is a particular kind of vector bundle.

Definition

Let $(M,g)$ be a Riemannian manifold, and $S\backslash subset\; M$ a Riemannian submanifold. Define, for a given $p\backslash in\; S$, a vector $n\backslash in\; T\_p\; S$ to be normal to $S$ whenever $g(n,s)=0$ for all $s\backslash in\; T\_p\; S$ (so that $n$ is orthogonal to $T\_pS$). The set $N\_pS$ of all such $n$ is then called the normal space to $S$ at $p$. Just as the tangent bundle to a manifold is constructed from all tangent spaces to the manifold, the normal bundle $NS$ to $S$ is defined as

$NS\; =\; \backslash coprod\_\{p\backslash in\; S\}N\_pS$.

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.

Differential topology | Fiber bundles

Нормальное расслоение