The Concept of Isotropy in Generalized Path-Spaces

This note attempts a generalization of the concept of isotropy for spaces defined by "paths", i.e. the solution curves of

xⁱ+αⁱ(x,x',t)=0; i=1,.......,n. xⁿ=dxⁱ/dt etc.                             (I)

Besides the tensor summation convention for repeated indices.