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A converse of the Gelfand theorem

Author: Yiping Mao
Journal: Proc. Amer. Math. Soc. 125 (1997), 2699-2702
MSC (1991): Primary 53C25, 53C30
MathSciNet review: 1401748
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Abstract: In this short note we obtain a converse to the Gelfand theorem: a Riemannian manifold is homogeneous if the isometrically invariant operators on the manifold form a commutative algebra.

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Additional Information

Yiping Mao
Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Address at time of publication: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208

Keywords: Invariant differential operator, homogeneous manifold
Received by editor(s): April 4, 1995
Received by editor(s) in revised form: April 30, 1996
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society