Abstract
We prove that the isometry group ℑ(\(\mathcal{N}\)) of an arbitrary Riemannian orbifold \(\mathcal{N}\), endowed with the compact-open topology, is a Lie group acting smoothly and properly on \(\mathcal{N}\). Moreover, ℑ(\(\mathcal{N}\)) admits a unique smooth structure that makes it into a Lie group. We show in particular that the isometry group of each compact Riemannian orbifold with a negative definite Ricci tensor is finite, thus generalizing the well-known Bochner’s theorem for Riemannian manifolds.
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The authors were supported by the Russian Foundation for Basic Research (Grant 06-01-00331-a).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 723–741, July–August, 2007.
Original Russian Text Copyright © 2007 Bagaev A. V. and Zhukova N. I.
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Bagaev, A.V., Zhukova, N.I. The isometry groups of Riemannian orbifolds. Sib Math J 48, 579–592 (2007). https://doi.org/10.1007/s11202-007-0060-y
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DOI: https://doi.org/10.1007/s11202-007-0060-y