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oai:docta.ucm.es:20.500.14352/422892025-12-10T13:03:48Zcom_20.500.14352_14col_20.500.14352_15

Algebras of differentiable functions on Riemannian manifolds Garrido Carballo, María Isabel Jaramillo Aguado, Jesús Ángel Rangel, Yenny C. For 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. 2023-06-20T00:15:40Z 2023-06-20T00:15:40Z 2023-06-20T00:15:40Z 2009-12 journal article https://hdl.handle.net/20.500.14352/42289 0024-6093 10.1112/blms/bdp077 eng info:eu-repo/grantAgreement/MEC//MTM2006-03531/ES/ANALISIS FUNCIONAL NO-LINEAL Y GEOMETRICO/ Garrido, Isabel, et al. «Algebras of Differentiable Functions on Riemannian Manifolds». Bulletin of the London Mathematical Society, vol. 41, n.o 6, diciembre de 2009, pp. 993-1001. DOI.org (Crossref), https://doi.org/10.1112/blms/bdp077 restricted access Oxford University Press