Skip Navigation



Bulletin of the London Mathematical Society Advance Access published online on September 23, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp077
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Garrido, I.
Right arrow Articles by Rangel, Y. C.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

Algebras of differentiable functions on Riemannian manifolds

Isabel Garrido

Departamento de Geometría y Topología
Universidad Complutense de Madrid
28040 Madrid
Spain

Jesús A. Jaramillo and Yenny C. Rangel

Departamento de Análisis Matemático
Universidad Complutense de Madrid
28040 Madrid
Spain
jaramil@mat.ucm.es
yenny.rangel@mat.ucm.es

Received 5 August 2008. Revision received 27 May 2009.

For an infinite-dimensional Riemannian manifold M we denote by CFormula(M) the space of all real bounded functions of class C1 on M with bounded derivative. In this paper we shall see how the natural structure of normed algebra on CFormula(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.

2000 Mathematics Subject Classification 58B20, 46E25, 54C35.

Research supported in part by D.G.I. (Spain) Grant MTM2006-03531.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.