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Algebras of differentiable functions on Riemannian manifolds


Garrido, M. Isabel and Jaramillo Aguado, Jesús Ángel and Rangel, Yenny C. (2009) Algebras of differentiable functions on Riemannian manifolds. Bulletin of the London Mathematical Society, 41 (6). pp. 993-1001. ISSN 0024-6093

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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.

Item Type:Article
Uncontrolled Keywords:Infinite-dimensional Riemannian manifold; metric and Riemannian isometries
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:16248

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Last Modified:27 May 2016 15:06

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