Garrido, M. IsabelJaramillo Aguado, Jesús ÁngelRangel, Yenny C.2023-06-202023-06-202009-120024-609310.1112/blms/bdp077https://hdl.handle.net/20.500.14352/42289For an infinite-dimensional Riemannian manifold M we denote by C1b(M) the space of all real bounded functions of class C(1) on M with bounded derivative. In this paper we shall see how the natural structure of normed algebra on C1b(M) characterizes the Riemannian structure of M, for the special case of the so-called uniformly bumpable manifolds. For that we need, among other things, to extend the classical Myers-Steenrod theorem on the equivalence between metric and Riemannian isometries, to the setting of infinite-dimensional Riemannian manifolds.engjournal articlehttp://blms.oxfordjournals.org/content/41/6/993.full.pdf+htmlhttp://www.cambridge.org/open access515.16Infinite-dimensional Riemannian manifoldmetric and Riemannian isometriesGeometria algebraica1201.01 Geometría Algebraica