nLab normal vector

Idea

Given an inner product space $(V, \langle -,-\rangle)$ then two vectors $v,w \in W$ are normal to each other if they are orthogonal to each other, in that their inner product vanishes: $\langle v,w\rangle = 0$.

Given an embedding of differentiable manifolds $i_X \colon X \hookrightarrow Y$ where $Y$carries Riemannian geometry structure, then the normal bundle of $i_X$ is the vector bundle of tangent vectors in $Y$ that are normal to tangent vectors of $X$.

Related entries

• orthonormal basis, orthogonal basis

  Gram-Schmidt process

• normal bundle, normally framed submanifold, Pontryagin's theorem

• orthogonality, orthogonal structure