标题： 古尔瑟斯类型（b）变换是邻域等距变换 显示英文标题

标题： Gurses' Type (b) Transformations are Neighborhood-Isometries

摘要： 借鉴C. G. 托雷（私人交流）给出的一个想法，我们证明了由Gürses类型(b)变换[M. Gürses, Phys. Rev. Lett. 70, 367 (1993)] 或等价地由托雷-安德森广义微分同胚[C. G. Torre 和 I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] 联系起来的黎曼空间(M,g)和(M,h)，是邻域等距的，即M中的每个点x都有一个对应的微分同胚phi，将x的邻域V映射到x的一般不同的邻域W上，使得phi*(h|W) = g|V。 显示英文摘要

摘要： 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.