Clifford bundle

In mathematics, a Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford algebra and whose local trivializations respect the algebra structure. There is a natural Clifford bundle associated to any (pseudo) Riemannian manifold M which is called the Clifford bundle of M.

This is commonly referred to as the Hopf fibration of S³, a topological construction pointed out by Heinz Hopf (1931). But Hopf’s procedure was explicitly based (with due reference) on an earlier geometrical construction of ‘Clifford parallels’.