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Gurses' Type (b) Transformations are Neighborhood-Isometries

I. Hauser·F. J. Ernst
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Abstract

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 Gurses type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or, equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] are neighborhood-isometric, i.e., every point x in M has a corresponding diffeomorphism phi of a neighborhood V of x onto a generally different neighborhood W of x such that phi*(h|W) = g|V.

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I. Hauser, F. J. Ernst. 1993-04-09. Gurses' Type (b) Transformations are Neighborhood-Isometries. https://doi.org/10.1103/physrevlett.71.316

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