In mathematics, a web permits an intrinsic characterization in terms of Riemannian geometry of the additive separation of variables in the Hamilton–Jacobi equation.
Given a smooth manifold of dimension n, an orthogonal web (also called orthogonal grid or Ricci’s grid) on a Riemannian manifold (M,g) is a set[3]
of n pairwise transversal and orthogonal foliations of connected submanifolds of dimension 1.
Since vector fields can be visualized as stream-lines of a stationary flow or as Faraday’s lines of force, a non-vanishing vector field in space generates a space-filling system of lines through each point, known to mathematicians as a congruence (i.e., a local foliation).
A systematic study of webs was started by Blaschke in the 1930s.
He extended the same group-theoretic approach to web geometry.
Of course, one may define a d-web of codimension r without having r as a divisor of the dimension of the ambient manifold.