nLab
normal vector

Contents

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

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

Given an embedding of differentiable manifolds i X:XYi_X \colon X \hookrightarrow Y where YYcarries Riemannian geometry structure, then the normal bundle of i Xi_X is the vector bundle of tangent vectors in YY that are normal to tangent vectors of XX.

Last revised on February 4, 2021 at 11:08:28. See the history of this page for a list of all contributions to it.