Following an idea close to one given by C. G. Torre (private communication), we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gürses’s type (b) transforamtion [M. Gürses, Phys. Rev. Lett. 70, 367 (1993)] or, equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and I. M. Anderson, Phys. Rev. Lett. 70, 3525 (1993)] are neighborhood isometric, i.e., every point x in M has a corresponding diffeomorphism φ of a neighborhood V of x onto a generally different neighborhood W of x such that ${\mathrm{\phi }}^{\mathrm{*}}$(h${\mathrm{\Vert }}_{\mathit{W}}$)=g${\mathrm{\Vert }}_{\mathit{V}}$.

• Received 13 April 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.316