A function of direction in a Weyl subspace associated with a set of orthogonal vector fields

Abstract

Let W-m be an m-dimensional subspace of an n-dimensional Weyl space W-n. Suppose that (1)v, (2)v,..., (m)v are mutually orthogonal smooth vector fields in W-m and that v is a non-tangential smooth vector field defined on W-m. Consider the (m + 1)-dimensional net delta defined by (1)v, (2)v, ..., (m)v, v. In this work, we obtain a function of direction associated with the net delta and define a class of curves on W-m in relation to this function of direction.